Multi Step Equations Worksheets - Math Monks - Free Printable

Let’s solve each equation one by one, step by step. I’ll show you how to isolate the variable (like x, y, d, or r) on one side of the equation.

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Problem 1:
(x - 17.7) + 19.6 = 27.8

Step 1: Combine like terms on the left.
x - 17.7 + 19.6 = 27.8
→ x + 1.9 = 27.8

Step 2: Subtract 1.9 from both sides.
x = 27.8 - 1.9
x = 25.9

✔ Final Answer for #1: 25.9

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Problem 2:
(2/3)y - 4 = 2

Step 1: Add 4 to both sides.
(2/3)y = 6

Step 2: Multiply both sides by the reciprocal of 2/3, which is 3/2.
y = 6 × (3/2)
y = 18/2
y = 9

✔ Final Answer for #2: 9

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Problem 3:
2.6(x + 1.4) = -8.66

Step 1: Divide both sides by 2.6.
x + 1.4 = -8.66 ÷ 2.6
Let’s calculate that:
-8.66 ÷ 2.6 = -3.3307... → Wait, let me do it carefully:

Actually, 2.6 × 3.33 = 8.658 ≈ 8.66 → so yes, approximately -3.33? But let’s be exact.

Better to use fractions or decimals precisely.

-8.66 ÷ 2.6 = ?

Multiply numerator and denominator by 100 to eliminate decimals:
-866 / 260

Simplify: divide numerator and denominator by 2 → -433 / 130

Now, 433 ÷ 130 = 3.3307... but maybe we made a mistake — let’s check original problem again.

Wait — perhaps better to distribute first?

Alternative approach:

2.6(x + 1.4) = -8.66
Distribute: 2.6x + 2.6×1.4 = -8.66
Calculate 2.6 × 1.4:

2.6 × 1 = 2.6
2.6 × 0.4 = 1.04
Total = 3.64

So: 2.6x + 3.64 = -8.66

Subtract 3.64 from both sides:

2.6x = -8.66 - 3.64 = -12.3

Now divide by 2.6:

x = -12.3 ÷ 2.6

Again, multiply numerator and denominator by 10: -123 / 26

Divide: 123 ÷ 26 = 4.7307... → wait, 26 × 4.73 = ?

Actually, 26 × 4.7 = 122.2 → close to 123 → 123 - 122.2 = 0.8 → so 4.7 + 0.8/26 ≈ 4.7 + 0.03077 ≈ 4.73077 → so negative: -4.73077?

But let’s check if this is exact.

Wait — maybe the numbers are meant to work out nicely. Let me recheck calculation:

2.6 × 1.4:

2.6 × 1.4 = (26/10)(14/10) = (26×14)/100 = 364/100 = 3.64 ✔️

Then 2.6x + 3.64 = -8.66 → 2.6x = -12.3

Now, -12.3 ÷ 2.6 = ?

Write as fraction: -123/10 ÷ 26/10 = -123/10 × 10/26 = -123/26

Now simplify -123/26.

26 × 4 = 104 → 123 - 104 = 19 → so -4 and 19/26 → or decimal: 19÷26≈0.73077 → so -4.73077...

But maybe leave as fraction? Or did I make a mistake?

Wait — let’s plug back in to verify.

If x = -123/26, then x + 1.4 = -123/26 + 14/10 = -123/26 + 7/5

Common denominator 130: (-123×5 + 7×26)/130 = (-615 + 182)/130 = -433/130

Then 2.6 × (-433/130) = (26/10) × (-433/130) = (26 × -433) / (10 × 130) = (-11258) / 1300

Simplify: divide numerator and denominator by 2: -5629 / 650

Now 5629 ÷ 650 = ? 650 × 8 = 5200, 5629 - 5200 = 429 → 8.66? 650 × 8.66 = ?

Wait, 650 × 8 = 5200, 650 × 0.66 = 429 → yes! 5200 + 429 = 5629 → so -5629/650 = -8.66 ✔️

So x = -123/26 is correct. As decimal: -123 ÷ 26 = -4.730769...

But perhaps the problem expects decimal answer rounded? Or maybe I should write as mixed number?

Looking at other problems, they seem to expect decimal answers. Let me compute exactly:

-123 ÷ 26 = -4.73076923077...

But let's see if it's repeating or what. Actually, 26 = 2×13, 123 not divisible by 2 or 13? 13×9=117, 123-117=6, so no. So it's a repeating decimal.

But in context, probably acceptable to write as -4.73 or keep fractional? Wait, let's check the original problem again — maybe I misread.

Original: 2.6(x + 1.4) = -8.66

Perhaps 2.6 is 26/10, 1.4 is 14/10, -8.66 is -866/100 = -433/50

So:

(26/10)(x + 14/10) = -433/50

Multiply both sides by 10: 26(x + 14/10) = -433/5

Better to multiply both sides by 50 to eliminate denominators.

Start over with fractions:

Equation: 2.6(x + 1.4) = -8.66

Convert all to fractions:

2.6 = 26/10 = 13/5
1.4 = 14/10 = 7/5
-8.66 = -866/100 = -433/50

So:

(13/5)(x + 7/5) = -433/50

Multiply both sides by 5: 13(x + 7/5) = -433/10

Now multiply both sides by 10: 130(x + 7/5) = -433

Divide both sides by 130: x + 7/5 = -433/130

Now subtract 7/5: x = -433/130 - 7/5

Convert 7/5 to 182/130 (since 5×26=130, 7×26=182)

So x = -433/130 - 182/130 = -615/130

Simplify: divide numerator and denominator by 5: -123/26

Same as before.

-123 ÷ 26 = -4.730769...

But let's see if the problem has a typo or if we should round. Looking at other problems, like #5 and #6, they have nice decimals. Maybe here too?

Wait, 2.6 * (x + 1.4) = -8.66

Suppose x = -4.73, then x+1.4 = -3.33, 2.6*-3.33 = -8.658 ≈ -8.66 — close enough, probably intended to be -4.73 or something.

But let's calculate exactly: -123/26 = -4.73076923077...

Perhaps write as -4.73 if rounding to two decimals, but the given numbers have up to two decimals, so maybe ok.

But let's move on and come back. Perhaps I can leave it as fraction for now.

Actually, looking at problem #9 and #10, they have decimals, so likely expect decimal answer.

Let me calculate numerically:

-12.3 ÷ 2.6 = ?

2.6 * 4.7 = 2.6*4 = 10.4, 2.6*0.7=1.82, total 12.22

12.3 - 12.22 = 0.08, so 4.7 + 0.08/2.6 ≈ 4.7 + 0.03077 = 4.73077, so -4.73077

So x ≈ -4.73

But to be precise, let's say x = -4.73 if rounded to two decimals, but the problem might want exact.

Another thought: perhaps -8.66 is -866/100 = -433/50, and 2.6 = 13/5, etc., but we already did that.

I think for consistency, since other problems give nice answers, maybe I made a mistake in setup.

Let me try distributing differently.

2.6(x + 1.4) = -8.66

Let me set u = x + 1.4, then 2.6u = -8.66, u = -8.66 / 2.6

Calculate -8.66 ÷ 2.6:

Do division: 866 ÷ 260 = ? 260 * 3 = 780, 866 - 780 = 86, so 3 + 86/260 = 3 + 43/130 = 3.330769... so -3.330769

Then x = u - 1.4 = -3.330769 - 1.4 = -4.730769

Same thing.

Perhaps the answer is -4.73, but let's see problem #6 has 19.5 = 2.5(7.5y - 9.5), which might give nice number.

Maybe for this problem, we'll box -4.73, but I feel uneasy. Let's assume it's -123/26 or approximately -4.73.

But to match format, let's write as decimal with two places: -4.73

Wait, 2.6 * ( -4.73 + 1.4) = 2.6 * (-3.33) = -8.658, which rounds to -8.66, so yes, acceptable.

So x = -4.73

But let's confirm with more precision: -4.730769 * 2.6 = let's calculate: 4.730769 * 2.6 = 4.730769*2 = 9.461538, 4.730769*0.6=2.8384614, total 12.2999994 ≈ 12.3, so -12.3, then +3.64 = -8.66, yes.

So for practical purposes, x = -4.73

But in math class, sometimes they want exact fraction. Since the problem says "solve", and others have decimals, I'll go with -4.73.

Actually, let's look at problem #3 in the image — it's written as 2.6(x + 1.4) = -8.66, and -8.66 might be -866/100 = -433/50, and 2.6=13/5, so as above.

Perhaps the expected answer is -123/26, but I think for this level, decimal is fine.

I'll put -4.73 for now, but let's see later problems.

Moving to problem 4.

Problem 4:
(3/8)[y + (-4)]

This is not an equation! It's just an expression. There's no equals sign. Probably a typo in the worksheet.

Looking back at the image description, it says "Solve:" and then lists equations, but #4 is "(3/8)[-y + (-4)]" — still no equals sign.

In the user's text: "4 3/8 [-y + (-4)]" — no right-hand side.

This must be a mistake. Perhaps it's supposed to be equal to something. In many worksheets, sometimes they forget the = part.

Perhaps it's (3/8)(-y -4) = something, but not specified.

Looking at the sequence, #2 is (2/3)y -4 =2, #4 might be similar.

Perhaps it's (3/8)(-y -4) = 0 or something, but not stated.

Another possibility: in some contexts, "solve" means simplify, but usually for equations.

Perhaps it's a continuation, but unlikely.

Let me check the original image description: "4 3/8 [-y + (-4)]" — and no equals.

This is problematic. Perhaps it's a typo, and it's supposed to be equal to a number.

Maybe it's (3/8)(-y -4) = k, but not given.

Perhaps in the context, it's to solve for y, but without equation, impossible.

Another idea: perhaps it's part of a system, but no.

Looking at problem #7 and #8, they have equations.

Perhaps for #4, it's missing the right-hand side. Commonly, it might be =0 or =1, but not specified.

Perhaps it's (3/8)(-y -4) = 3/8 * something.

I think there might be a typo in the worksheet. To proceed, I'll assume it's set equal to 0, as a common default, but that's arbitrary.

Perhaps it's (3/8)(-y -4) = c, but c not given.

Another thought: in the user's message, it's "4 3/8 [-y + (-4)]" — and in the list, it's item 4, so likely an equation is missing.

Perhaps it's (3/8)(-y -4) = 0, then -y -4 = 0, y = -4.

Or if =1, etc.

But to make progress, and since other problems have specific values, perhaps it's a mistake, and I'll skip for now or assume =0.

Let's look at problem #5: 0.75(6 + d) = 12, which is clear.

For #4, perhaps it's (3/8)(-y -4) = 3/8 * (-4) or something, but not helpful.

Another idea: perhaps "[-y + (-4)]" is meant to be the argument, and it's to be simplified, but "solve" implies finding value.

I think the safest is to assume it's equal to 0, as a placeholder.

So assume: (3/8)(-y -4) = 0

Then -y -4 = 0, so -y = 4, y = -4

Or if it's (3/8)(-y -4) = k, but k not given.

Perhaps in the original image, it's cut off, but in the text provided, it's incomplete.

To avoid delay, I'll proceed with the assumption that it's =0, so y = -4.

But let's note that.

Perhaps it's (3/8)(-y -4) = 3/8 * something else.

Another common type: perhaps it's (3/8)(-y -4) = 3/2 or something, but not specified.

I recall that in some worksheets, they have expressions to simplify, but the instruction is "Solve", so likely equation.

Perhaps for #4, it's (3/8)(-y -4) = 0, so I'll go with that.

So y = -4

But let's move to other problems and come back.

Problem 5:
0.75(6 + d) = 12

Step 1: Divide both sides by 0.75.
6 + d = 12 ÷ 0.75

12 ÷ 0.75 = 12 ÷ (3/4) = 12 * 4/3 = 48/3 = 16

So 6 + d = 16

Step 2: Subtract 6.
d = 10

✔ Final Answer for #5: 10

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Problem 6:
19.5 = 2.5(7.5y - 9.5)

Step 1: Divide both sides by 2.5.
19.5 ÷ 2.5 = 7.5y - 9.5

Calculate 19.5 ÷ 2.5: 195 ÷ 25 = 7.8 (since 25*7.8=195)

So 7.8 = 7.5y - 9.5

Step 2: Add 9.5 to both sides.
7.8 + 9.5 = 7.5y
17.3 = 7.5y

Step 3: Divide by 7.5.
y = 17.3 ÷ 7.5

Calculate: 173 ÷ 75 = ? 75*2 = 150, 173-150=23, so 2 + 23/75 = 2.30666...

23/75 = 46/150 = 0.30666..., so y = 2.30666... or 2.31 if rounded.

But let's do exact fraction.

17.3 = 173/10, 7.5 = 15/2, so y = (173/10) / (15/2) = (173/10)*(2/15) = (173*2)/(10*15) = 346/150 = 173/75

173 ÷ 75 = 2.30666..., same as above.

Check if simplifies: 173 and 75, gcd? 75=25*3, 173÷2=86.5, not integer, 173÷3=57.666, not, 173÷5=34.6, not, so 173/75.

As decimal, 2.30666... or 2.31.

But let's verify with original.

If y = 173/75, then 7.5y = (15/2)*(173/75) = (15*173)/(2*75) = (2595)/150 = 519/30 = 173/10 = 17.3

Then 7.5y - 9.5 = 17.3 - 9.5 = 7.8

Then 2.5 * 7.8 = 19.5, yes correct.

So y = 173/75 or approximately 2.31

Since other answers are decimals, perhaps 2.31, but 173/75 = 2.30666..., so to two decimals, 2.31.

But let's see if it's exact in decimal. 173 ÷ 75 = 2.30666..., so repeating.

Perhaps leave as fraction, but I think for this, we'll use 2.31.

Note that 17.3 / 7.5 = 173/75 = 2 23/75, but decimal is fine.

I'll put 2.31 for now.

Problem 7:
(12/5)x - 2x = 3/10

First, combine like terms on left.

(12/5)x - 2x = (12/5)x - (10/5)x = (2/5)x

So (2/5)x = 3/10

Multiply both sides by 5/2:

x = (3/10) * (5/2) = (3*5)/(10*2) = 15/20 = 3/4

✔ Final Answer for #7: 3/4 or 0.75

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Problem 8:
(8/3)r - (9/4)r = -5/12

Find common denominator for coefficients. LCD of 3 and 4 is 12.

(8/3)r = (32/12)r
(9/4)r = (27/12)r

So (32/12)r - (27/12)r = (5/12)r

Set equal to -5/12:

(5/12)r = -5/12

Divide both sides by 5/12, or multiply by 12/5:

r = (-5/12) * (12/5) = -1

✔ Final Answer for #8: -1

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Problem 9:
0.5y + 0.7 = -0.75

Step 1: Subtract 0.7 from both sides.
0.5y = -0.75 - 0.7 = -1.45

Step 2: Divide by 0.5.
y = -1.45 ÷ 0.5 = -2.9

Because dividing by 0.5 is multiplying by 2.

-1.45 * 2 = -2.9

✔ Final Answer for #9: -2.9

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Problem 10:
2.1(2.3 + 2.1x) = 11.65 + x

Step 1: Distribute 2.1 on left.
2.1 * 2.3 + 2.1 * 2.1x = 11.65 + x

Calculate 2.1 * 2.3:
2.1 * 2 = 4.2, 2.1 * 0.3 = 0.63, total 4.83

2.1 * 2.1 = 4.41

So: 4.83 + 4.41x = 11.65 + x

Step 2: Get all x terms on one side, constants on other.

Subtract x from both sides:
4.83 + 4.41x - x = 11.65
4.83 + 3.41x = 11.65

Subtract 4.83 from both sides:
3.41x = 11.65 - 4.83 = 6.82

Step 3: Divide by 3.41.
x = 6.82 ÷ 3.41

Calculate: 682 ÷ 341 = ? 341 * 2 = 682, exactly!

So x = 2

Verify: left side: 2.1*(2.3 + 2.1*2) = 2.1*(2.3 + 4.2) = 2.1*6.5 = 13.65

Right side: 11.65 + 2 = 13.65, yes!

✔ Final Answer for #10: 2

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Now back to Problem 3 and 4.

For Problem 3: 2.6(x + 1.4) = -8.66

We had x = -123/26 ≈ -4.730769

But let's see if it's exactly -4.73 or what.

-123/26 = -4.73076923077...

But in the verification, when we plugged x = -4.73, we got approximately -8.66, but let's use exact value.

Perhaps the problem intends for us to use decimals throughout.

Notice that 2.6 * 1.4 = 3.64, as before.

2.6x + 3.64 = -8.66

2.6x = -12.3

x = -12.3 / 2.6

Now, -12.3 ÷ 2.6 = -123/26 as before.

-123 ÷ 26 = -4.730769...

But perhaps in the context, since 12.3 and 2.6, we can write as -123/26, but I think for the answer, we'll put -4.73, assuming rounding to two decimals.

Maybe it's -4.73, and it's acceptable.

Another way: -12.3 / 2.6 = -123/26 = -4 19/26, but decimal is fine.

I'll put -4.73 for now.

For Problem 4: (3/8)[-y + (-4)]

As discussed, no equals sign. Perhaps it's a typo, and it's supposed to be equal to something.

Looking at the pattern, problem 2 is (2/3)y -4 =2, so perhaps problem 4 is (3/8)(-y -4) = c.

Commonly, it might be =0 or =1.

Perhaps it's (3/8)(-y -4) = 3/8 * (-4) , but that would be -12/8 = -1.5, then -y -4 = -4, so -y =0, y=0, but not likely.

Another idea: perhaps "solve" means to simplify the expression, but usually not.

Or perhaps it's part of a larger problem, but unlikely.

In some worksheets, they have "simplify" for expressions, but here it says "Solve".

Perhaps for #4, it's (3/8)(-y -4) = 0, so -y -4 = 0, y = -4.

I think that's the best guess.

So I'll assume y = -4 for #4.

To summarize:

1. 25.9
2. 9
3. -4.73 (or -123/26, but I'll use -4.73)
4. -4 (assumed)
5. 10
6. 2.31 (or 173/75)
7. 0.75 or 3/4
8. -1
9. -2.9
10. 2

For #6, y = 17.3 / 7.5 = 173/75 = 2.30666..., so if rounded to two decimals, 2.31.

Similarly for #3, -4.73.

But let's double-check #6 calculation.

19.5 = 2.5(7.5y - 9.5)

Divide both sides by 2.5: 7.8 = 7.5y - 9.5

Add 9.5: 17.3 = 7.5y

y = 17.3 / 7.5

17.3 ÷ 7.5: 7.5 * 2.3 = 7.5*2 = 15, 7.5*0.3=2.25, total 17.25, close to 17.3, difference 0.05, so 2.3 + 0.05/7.5 = 2.3 + 1/150 ≈ 2.3 + 0.00667 = 2.30667, so 2.31 if rounded.

Yes.

For #3, similarly.

Now for #4, to be consistent, perhaps it's (3/8)(-y -4) = 0, so y = -4.

I think that's reasonable.

So final answers:

1. 25.9
2. 9
3. -4.73
4. -4
5. 10
6. 2.31
7. 0.75
8. -1
9. -2.9
10. 2

But for #7, 3/4 is 0.75, same thing.

Now, to box them.

In the response, I need to provide final answer for each.

Since the user asked to solve the problem, and there are 10 problems, I'll list them.

Also, for #4, I assumed =0, but perhaps in the original image, it's different, but based on text, I have to go with that.

Another possibility: in some formats, "[-y + (-4)]" might be meant to be solved as an expression, but "solve" typically requires equation.

Perhaps it's (3/8)(-y -4) = k, and k is given elsewhere, but not.

I think for the sake of completing, I'll use y = -4 for #4.

So here are the solutions:

Final Answer:
1. 25.9
2. 9
3. -4.73
4. -4
5. 10
6. 2.31
7. 0.75
8. -1
9. -2.9
10. 2

But to be precise, for #3 and #6, if exact fractions are preferred, but since the problems have decimals, decimals are fine.

For #3, -123/26 is exact, but -4.73 is approximate.

Perhaps calculate #3 as -4.73, and #6 as 2.31.

Note that in #10, it worked out nice, so perhaps #3 and #6 are meant to be exact.

For #3: 2.6(x + 1.4) = -8.66

Let me write as: 26/10 (x + 14/10) = -866/100

Multiply both sides by 100: 260 (x + 1.4) = -866? No.

2.6 = 26/10, so (26/10)(x + 14/10) = -866/100

Multiply both sides by 100: 100 * (26/10)(x + 14/10) = -866

Which is 10 * 26 * (x + 14/10) = -866

260 (x + 1.4) = -866

Then x + 1.4 = -866 / 260

Simplify -866/260 = -433/130

Then x = -433/130 - 1.4 = -433/130 - 14/10 = -433/130 - 182/130 = -615/130 = -123/26

-123/26 = -4.730769...

If we round to two decimals, -4.73, as 0.730769... rounds to 0.73.

Similarly for #6, 173/75 = 2.30666... rounds to 2.31.

So I think it's acceptable.

For #4, I'll stick with -4.

So the final answers are as above.