Which simplified algebraic expression corresponds to each unsimplified expression? Match e… — Armed Services Vocational Aptitude Battery (ASVAB)

Which simplified algebraic expression corresponds to each unsimplified expression? Match each item on the left with its correctly simplified equivalent on the right.

$4x + 3x - 5$ $7x - 5$
$2(3x + 4)$ $6x + 8$
$9x - 4x + 2$ $5x + 2$
$3(x - 2) + 5$ $3x - 1$

Answer

The correct pairings are:

4x + 3x - 5

matches with

7x - 5

;

2(3x + 4)

matches with

6x + 8

;

9x - 4x + 2

matches with

5x + 2

; and

3(x - 2) + 5

matches with

3x - 1

Each expression is correctly matched to its simplified equivalent by strictly applying the distributive property to eliminate any grouping symbols, followed by combining like terms (terms with identical variables) and grouping constants.

Step-by-Step Solution

Simplify the first expression,

4x + 3x - 5

7x - 5

Combining the like variable terms (

4x

and

3x

) gives

7x

. The constant

-5

remains unchanged.

Simplify the second expression,

2(3x + 4)

6x + 8

Applying the distributive property multiplies each term inside the parentheses by

2

Simplify the third expression,

9x - 4x + 2

5x + 2

Combining the like variable terms (

9x

and

-4x

) gives

5x

. The constant

2

remains unchanged.

Simplify the fourth expression,

3(x - 2) + 5

3x - 1

Distributing the

3

yields

3x - 6

. Combining the constant terms (

-6

and

5

) results in

-1

Key Concept

Simplifying Algebraic Expressions by Combining Like Terms and Distributing

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic