Question

1. Which expression is equivalent to 2x+3y+4x

a. 9xy b. 18xy c. 5x+3y d. 6x+3y

2. Which expression is equivalent to 4(2x-3)

a. 2x-12 b. 6x+1 c. 8x-3 d. 8x-12

Answer 1

To simplify the expression 2x+3y+4x, combine the like terms to get 6x+3y. To simplify 4(2x-3), distribute 4 to each term inside the parentheses to get 8x-12.

Step-by-step explanation:

To simplify the expression 2x+3y+4x, we can combine like terms. Like terms have the same variable(s) raised to the same exponent(s). In this expression, the like terms are both x terms: 2x and 4x. When we combine these terms, we add their coefficients. So, 2x+4x simplifies to 6x.

The expression 2x+3y+4x simplifies to 6x+3y. Therefore, the correct option is 6x+3y.

To simplify the expression 4(2x-3), we can distribute the 4 to each term inside the parentheses. So, 4 times 2x is 8x, and 4 times -3 is -12. Therefore, 4(2x-3) simplifies to 8x-12. Hence, the correct option is 8x-12.

Answer 2

Question 1 Which expression is equivalent to 2x+3y+4x?

Here we have three numbers being multiplied by a variable.
We can simplify the expression here...but how is it done?
Well, the variable works sort of like a unit here...say we had
2 apples + 3 oranges + 4 apples.
We would then simplify to
6 apples + 3 oranges.

Variables are combined in the same way...you can only do it if you have the same variables. This is called combining like terms.


`\mathsf{2x+3y+4x=\boxed{\mathsf{6x+3y}}}`

Question 2 Which expression is equivalent to 4(2x-3)?

Here, we use what is called the distributive property.
Say we had 4 baskets, each with 2 apples and 3 oranges.
We can conclude that there are 4×2 apples and 4×3 oranges.
You multiply to both terms inside the parentheses!


`\mathsf{4(2x-3)}=\mathsf{4(2x)+4(-3)}=\boxed{\mathsf{8x-12}}`