Simplifying Expressions worksheet with eight algebraic problems.

Let’s solve each expression step by step. We’ll combine like terms and use the distributive property where needed.

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1. 5x + 2x

These are both “x” terms, so we add them:

5x + 2x = 7x

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2. 3x – 5 + 2x

Combine the x terms first:
3x + 2x = 5x
Then keep the -5 as is.

So:
5x – 5 → 5x - 5

*(We can’t combine 5x and -5 because one has a variable and the other doesn’t.)*

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3. 4(x – 2)

Use distributive property: multiply 4 by both inside terms.

4 × x = 4x
4 × (-2) = -8

So:
4x - 8

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4. 6 + 2(x + 1)

First, distribute the 2 into (x + 1):

2 × x = 2x
2 × 1 = 2

Now rewrite:
6 + 2x + 2

Combine constants: 6 + 2 = 8

So:
2x + 8

*(Order doesn’t matter — you could write 8 + 2x too, but usually we put variable term first.)*

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5. 7x + 2 – 5x + 3

Group like terms:

x terms: 7x – 5x = 2x
constants: 2 + 3 = 5

So:
2x + 5

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6. 2(x + 3) – 2x

Distribute the 2 first:

2 × x = 2x
2 × 3 = 6

So now:
2x + 6 – 2x

Now combine x terms: 2x – 2x = 0x → they cancel out!

Left with:
6

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7. 3x + 2 – y + 4

Group like terms:

x terms: 3x
y terms: -y (only one)
constants: 2 + 4 = 6

So:
3x - y + 6

*(We can’t combine x and y — different variables.)*

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8. 2y + x + 5x – 6y

Group like terms:

x terms: x + 5x = 6x
y terms: 2y – 6y = -4y

No constants.

So:
6x - 4y

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✔ All done! Let me double-check each one quickly:

1. 5x+2x=7x ✔️
2. 3x+2x-5=5x-5 ✔️
3. 4x-8 ✔️
4. 6+2x+2=2x+8 ✔️
5. 7x-5x=2x; 2+3=5 → 2x+5 ✔️
6. 2x+6-2x=6 ✔️
7. 3x - y + 6 ✔️
8. x+5x=6x; 2y-6y=-4y → 6x-4y ✔️

All correct!

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Final Answer:
1. 7x
2. 5x - 5
3. 4x - 8
4. 2x + 8
5. 2x + 5
6. 6
7. 3x - y + 6
8. 6x - 4y