Question

Use the algebraic rules to determine which expression is equivalent to –5x + 4.

A. (-3x) + 3 + (-2x) + 1
B. (-3x) + 3 + (2x) + 1
C. 3x + 3 + 2x + 1
D. (-3x) + (-3) + (-2x) + (-1)

Answer 1

Option A (-3x) + 3 + (-2x) + 1 is equivalent to –5x + 4, as it simplifies to the same expression when like terms are combined.

Step-by-step explanation:

To determine which expression is equivalent to –5x + 4, we can combine like terms from the given options. Let's break down the options one by one:

• A. (-3x) + 3 + (-2x) + 1 = -3x - 2x + 3 + 1 = -5x + 4
• B. (-3x) + 3 + (2x) + 1 = -3x + 2x + 3 + 1 = -x + 4
• C. 3x + 3 + 2x + 1 = 3x + 2x + 3 + 1 = 5x + 4
• D. (-3x) + (-3) + (-2x) + (-1) = -3x - 2x - 3 - 1 = -5x - 4

After simplifying, we can see that option A is the expression that is equivalent to –5x + 4 because the terms –3x and –2x add up to –5x and the constants 3 and 1 add up to 4.