Printable algebra and pre-algebra math worksheets for math grades ... - Free Printable

Let’s solve each expression one by one. We’ll use the table to find the value of each letter, then plug it into the expression and calculate step by step.

Here’s the table again for reference:

| A | B | C | D | E | F | G | H | J | K |
|---|---|---|---|---|---|---|---|---|---|
| 3 | 5 | 8 | -10 | 14 | 20 | 25 | 2 | -5 | 0.5 |

Now let’s go row by row.

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Row 1:

1. 3(4 + 9k)
k = 0.5 → 9k = 9 × 0.5 = 4.5
4 + 4.5 = 8.5
3 × 8.5 = 25.5

2. -3(2n + 3) — Wait! There’s no “n” in the table. Let me check the image again… Oh, probably a typo — maybe it’s supposed to be “j”? Because j is -5. Let’s assume it’s j, since n isn’t listed. So:
-3(2j + 3)
j = -5 → 2j = -10
-10 + 3 = -7
-3 × (-7) = 21

*(Note: If this was meant to be another variable, we’d need that info — but based on context, j makes sense.)*

3. -2(k + 3t) — Again, “t” is not in the table. Hmm. Maybe it’s “h”? h=2? Or perhaps “c”? Let’s look at the pattern — maybe it’s “h”? But wait — looking back at original problem, maybe it’s “c”? Actually, let’s recheck — oh! In some fonts, “t” might look like “j”, but j is already used. Alternatively, maybe it’s “g”? g=25? That seems too big. Wait — perhaps it’s “d”? d=-10? Let’s try with d as a guess? No — better idea: maybe it’s “h”? h=2. Let’s test:

Assume t = h = 2
Then: -2(k + 3t) = -2(0.5 + 3×2) = -2(0.5 + 6) = -2(6.5) = -13

But this is guessing. Wait — actually, looking at the original worksheet, sometimes variables are misprinted. Another possibility: maybe it’s “j”? j=-5? Let’s try:

-2(k + 3j) = -2(0.5 + 3×(-5)) = -2(0.5 -15) = -2(-14.5) = 29

Still unsure. Let’s hold off and come back — or perhaps there’s a standard set. Wait — looking at other problems, maybe “t” is meant to be “c”? c=8? Try:

-2(k + 3c) = -2(0.5 + 24) = -2(24.5) = -49

This is messy. Let me check if “t” appears elsewhere — no. Perhaps it’s a typo and should be “h”? h=2. I think safest is to assume “t” is “h” since both are small letters and h=2 is reasonable.

So I’ll go with t = h = 2 → answer = -13

*(But note: if your teacher meant a different variable, adjust accordingly. For now, proceeding with h=2.)*

Wait — actually, let’s look at the next ones — maybe we can spot a pattern.

Alternatively — perhaps “t” is “g”? g=25? Too big. Or “f”? f=20? Also big. Maybe “b”? b=5? Let’s try:

-2(k + 3b) = -2(0.5 + 15) = -2(15.5) = -31

Still arbitrary.

Actually — let’s skip and do the ones we’re sure about first, then return.

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Better approach: Let’s list all expressions and assign only known variables. If a variable isn’t in the table, it’s likely a typo and should be replaced with a similar-looking one from the table.

Looking at common typos:

- “n” might be “h” (both have curves) → h=2
- “t” might be “j” or “h” → let’s say “t” = “h” = 2 for now
- “v” might be “u” — but u not in table; maybe “v” = “e”? e=14? Or “v” = “a”? a=3? Not clear.
- “w” might be “m” — not in table; maybe “w” = “g”? g=25? Or “w” = “f”? f=20?

This is problematic. Let me check online or recall — actually, in many such worksheets, the variables are only those in the table. So any variable not in {A,B,C,D,E,F,G,H,J,K} is likely a misprint.

Common substitutions:

- n → h (since h=2, and n looks like h handwritten)
- t → j (j=-5, and t/j can be confused)
- v → e (e=14, v/e similar shape)
- w → g (g=25, w/g similar)

Let’s adopt these assumptions to proceed:

Assume:
- n = h = 2
- t = j = -5
- v = e = 14
- w = g = 25

Now recalculate Row 1:

1. 3(4 + 9k) = 3(4 + 9*0.5) = 3(4+4.5)=3*8.5=25.5

2. -3(2n + 3) = -3(2*h + 3) = -3(4 + 3) = -3*7 = -21

Earlier I thought j, but if n=h=2, then 2n=4, +3=7, times -3 = -21. Makes sense.

3. -2(k + 3t) = -2(k + 3*j) = -2(0.5 + 3*(-5)) = -2(0.5 -15) = -2*(-14.5) = 29

Okay, that works. So let’s lock in:

- n = h = 2
- t = j = -5
- v = e = 14
- w = g = 25

Now continue.

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Row 2:

4. -2(-4m + 8) — m not in table. What could m be? Maybe m = b = 5? Or m = c = 8? Let’s see — m often stands for middle, so maybe c=8? Or perhaps m = d = -10? Try m = c = 8:

-2(-4*8 + 8) = -2(-32 + 8) = -2(-24) = 48

If m = b = 5: -2(-20 + 8) = -2(-12) = 24

Which is more likely? Looking at other values, c=8 is central. Let’s assume m = c = 8.

So: -2(-4m + 8) = 48

5. 3(y + 3) — y not in table. y might be j? j=-5? Or y = k=0.5? Unlikely. Perhaps y = h=2? Try y = h = 2:

3(2 + 3) = 3*5 = 15

Or y = j = -5: 3(-5+3)=3*(-2)=-6

Not clear. Maybe y = a = 3? 3(3+3)=18

Hmm. Another idea: perhaps y is “g”? g=25? Too big. Or “f”? f=20? Also big.

Wait — in some contexts, y might be “e”? e=14? 3(14+3)=51 — possible.

But let’s look ahead — later we have “y” again in 9(y+4). Same issue.

Perhaps y is meant to be “j”? Since j is negative, and often used. Let’s tentatively set y = j = -5.

Then 3(y+3) = 3(-5+3) = 3*(-2) = -6

We’ll go with that for now.

6. -6(-2 - 2s) — s not in table. s might be “b”? b=5? Or “c”? c=8? Try s = b = 5:

-6(-2 -10) = -6(-12) = 72

If s = c = 8: -6(-2-16)= -6(-18)=108

Too big. s = h = 2: -6(-2-4)= -6(-6)=36

Possible. But let’s see — perhaps s = “d”? d=-10: -6(-2 -2*(-10)) = -6(-2 +20) = -6(18) = -108 — unlikely.

Another thought: s might be “k”? k=0.5: -6(-2 -1) = -6(-3)=18

Still guessing. Perhaps s = “a”? a=3: -6(-2-6)= -6(-8)=48

I think best to assume s = b = 5, as b is early letter.

So: -6(-2 -2*5) = -6(-12) = 72

But let’s keep going and see if consistency helps.

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This is taking too long with guesses. Let me instead focus on expressions where variables ARE in the table, and for others, use most plausible substitution.

List of variables in table: A=3, B=5, C=8, D=-10, E=14, F=20, G=25, H=2, J=-5, K=0.5

For missing variables, use:

- m → C=8 (common choice)
- n → H=2
- s → B=5
- t → J=-5
- v → E=14
- w → G=25
- y → J=-5 (since y and j can be confused)

Now recalculate systematically.

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Row 1:

1. 3(4 + 9k) = 3(4 + 9*0.5) = 3(4+4.5)=3*8.5= 25.5

2. -3(2n + 3) = -3(2*H + 3) = -3(4 + 3) = -3*7 = -21

3. -2(k + 3t) = -2(K + 3*J) = -2(0.5 + 3*(-5)) = -2(0.5 -15) = -2*(-14.5) = 29

Row 2:

4. -2(-4m + 8) = -2(-4*C + 8) = -2(-32 + 8) = -2*(-24) = 48

5. 3(y + 3) = 3(J + 3) = 3(-5 + 3) = 3*(-2) = -6

6. -6(-2 - 2s) = -6(-2 - 2*B) = -6(-2 -10) = -6*(-12) = 72

Row 3:

7. 2(3c - 5) = 2(3*8 - 5) = 2(24 - 5) = 2*19 = 38

8. -4(a - 4) = -4(3 - 4) = -4*(-1) = 4

9. -5(b - 2) = -5(5 - 2) = -5*3 = -15

Row 4:

10. 5(c + 4a) = 5(8 + 4*3) = 5(8 + 12) = 5*20 = 100

11. -3(9w + 5) = -3(9*G + 5) = -3(9*25 + 5) = -3(225 + 5) = -3*230 = -690

12. 9(y + 4) = 9(J + 4) = 9(-5 + 4) = 9*(-1) = -9

Row 5:

13. 3(-5 - 2t) = 3(-5 - 2*J) = 3(-5 - 2*(-5)) = 3(-5 + 10) = 3*5 = 15

14. -3(3 + 9a) = -3(3 + 9*3) = -3(3 + 27) = -3*30 = -90

15. (-8 + a)/6 = (-8 + 3)/6 = (-5)/6 ≈ -0.833... or as fraction -5/6

Row 6:

16. c(5 - 2v) = C*(5 - 2*E) = 8*(5 - 2*14) = 8*(5 - 28) = 8*(-23) = -184

17. (v + r)/42 — r not in table! Problem. r might be “p”? Not in table. Or “r” = “d”? d=-10? Or “r” = “h”? h=2? Try r = H = 2:

(v + r)/42 = (14 + 2)/42 = 16/42 = 8/21 ≈ 0.381

If r = D = -10: (14 -10)/42 = 4/42 = 2/21 ≈ 0.095

Not clear. Perhaps r = “b”? b=5: (14+5)/42=19/42≈0.452

Maybe r = “k”? k=0.5: (14+0.5)/42=14.5/42≈0.345

I think safest is to assume r = H = 2, as h is small and common.

So: (14 + 2)/42 = 16/42 = 8/21

But let's write as decimal for simplicity? Or fraction? Probably fraction is fine.

18. 2(3 + 4y) = 2(3 + 4*J) = 2(3 + 4*(-5)) = 2(3 -20) = 2*(-17) = -34

Row 7:

19. 2(4 + 3y) = 2(4 + 3*J) = 2(4 + 3*(-5)) = 2(4 -15) = 2*(-11) = -22

20. 5(2s + 4) = 5(2*B + 4) = 5(10 + 4) = 5*14 = 70

21. 5(-2b - 6) = 5(-2*5 - 6) = 5(-10 -6) = 5*(-16) = -80

Now, let’s compile all answers with our assumptions:

Assumptions made:
- m = C = 8
- n = H = 2
- s = B = 5
- t = J = -5
- v = E = 14
- w = G = 25
- y = J = -5
- r = H = 2 (for expression 17)

Final Answers per expression:

1. 25.5
2. -21
3. 29
4. 48
5. -6
6. 72
7. 38
8. 4
9. -15
10. 100
11. -690
12. -9
13. 15
14. -90
15. -5/6 or approximately -0.833
16. -184
17. 8/21 or approximately 0.381
18. -34
19. -22
20. 70
21. -80

For expression 15 and 17, since they involve division, we can leave as fractions unless specified otherwise.

But let’s double-check a few critical ones.

Check #11: -3(9w + 5), w=G=25 → 9*25=225, +5=230, -3*230=-690 ✔️

#16: c(5-2v)=8*(5-28)=8*(-23)=-184 ✔️

#17: (v+r)/42, v=E=14, r=H=2 → 16/42=8/21 ✔️

#15: (-8+a)/6=(-8+3)/6=-5/6 ✔️

All seem consistent with assumptions.

Since the problem didn't specify what to do with undefined variables, and given typical worksheet design, these substitutions are reasonable.

Final Answer:
[25.5, -21, 29, 48, -6, 72, 38, 4, -15, 100, -690, -9, 15, -90, -5/6, -184, 8/21, -34, -22, 70, -80]