Combine Like Terms: Mastering Equivalent Expressions

1. Sarah has 3x + 5 apples and her friend gives her 2x + 3 more apples. How many apples does she have in total? Combine like terms to find the answer.

• 6x + 5

• 5x + 8

• 4x + 7

• 3x + 3

2. A rectangle has a length of 4x + 2 and a width of 3x + 5. What is the expression for the perimeter of the rectangle? Simplify your answer.

• 12x + 10

• 10x + 12

• 14x + 14

• 8x + 6

3. If 2(3x + 4) = 6x + 8, are these expressions equivalent? Explain your reasoning.

• No, the expressions are not equivalent.

• Yes, but only under certain conditions.

• The expressions are equivalent only if x = 0.

• Yes, the expressions are equivalent.

4. Tom bought 5 packs of pencils, each containing 2x + 3 pencils. Write an expression for the total number of pencils he bought and simplify it by combining like terms.

• 6x + 9

• 4x + 6

• 8x + 12

• 10x + 15

5. The expression 4(x + 2) + 3(x - 1) can be simplified. What is the simplified expression? Use the distributive property and combine like terms.

• 8x + 3

• 5x + 8

• 7x + 5

• 6x + 4

6. A store sells notebooks for 2x + 4 dollars each and pens for 3x + 2 dollars each. Write an expression for the total cost of buying 4 notebooks and 5 pens, then simplify it.

• 23x + 26

• 20x + 30

• 25x + 20

• 22x + 24

7. If you have the expression 5x + 3 - 2x + 7, what is the simplified form? Combine like terms to find your answer.

• 5x + 10

• 2x + 5

• 3x + 10

• 3x + 5

8. A gardener has 2x + 6 flowers and buys 3x + 4 more. Write an expression for the total number of flowers and simplify it.

• 5x + 10

• 4x + 8

• 2x + 4

• 6x + 10

9. The expression 6(x - 1) + 2(2x + 3) can be simplified. What is the final expression after applying the distributive property and combining like terms?

• 4x + 9

• 10x

• 12x + 3

• 8x + 6

10. If 3(2x + 5) = 6x + 15, are these two expressions equivalent? Justify your answer with steps.

• No, the expressions are not equivalent.

• The expressions are equivalent, but only for certain values of x.

• The left side simplifies to 6x + 10, making them unequal.

• Yes, the expressions are equivalent.