If the expression 5(2x - 3) - 4(x - 2) is equivalent to ax + b for all values of x, where … — SAT

If the expression $5(2x - 3) - 4(x - 2)$ is equivalent to $ax + b$ for all values of $x$ , where $a$ and $b$ are constants, what is the value of $a$ ?

Answer: 6

Answer

The value of the constant coefficient is 6.

Expanding the expression

5(2x - 3) - 4(x - 2)

yields

10x - 15 - 4x + 8

. Combining the like terms results in

(10x - 4x) + (-15 + 8) = 6x - 7

. Comparing this to the expression

ax + b

, the constant coefficient

a

is equal to 6.

Step-by-Step Solution

Distribute the multipliers to the terms inside the parentheses.

10x - 15 - 4x + 8

To remove the parentheses and prepare the expression for simplification, multiply each term inside

(2x - 3)

5

and each term inside

(x - 2)

-4

Combine the linear terms and the constant terms.

6x - 7

Combine the variable terms (

10x - 4x = 6x

) and the constants (

-15 + 8 = -7

) to rewrite the expression in its simplest form.

Compare the simplified expression to the form

ax + b

to identify the value of

a

a = 6

The coefficient of the variable

x

6x - 7

corresponds directly to

a

ax + b

Key Concept

Equivalent Algebraic Expressions

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