Which expression is equivalent to 3(2x - 5) - (x - 4)? — SAT

Which expression is equivalent to $3(2x - 5) - (x - 4)$ ?

5x - 11

To find the equivalent expression, apply the distributive property to both parts of the expression:

3(2x - 5)

expands to

6x - 15

, and

-(x - 4)

expands to

-x + 4

. Combining the variable terms gives

6x - x = 5x

. Combining the constant terms gives

-15 + 4 = -11

. Thus, the simplified equivalent expression is

5x - 11

Distribute the number

3

to each term inside the first set of parentheses.

3(2x - 5) = 6x - 15

To eliminate the first set of parentheses by applying the distributive property.

Distribute the negative sign (equivalent to multiplying by

-1

) to each term inside the second set of parentheses.

-(x - 4) = -x + 4

To eliminate the second set of parentheses, ensuring the negative sign is applied to both

x

and

-4

Combine the like terms (the variable terms and the constant terms).

(6x - x) + (-15 + 4) = 5x - 11

To simplify the expression into its final equivalent form.

Equivalent Algebraic Expressions

Question