Question

writing about determining equivalent expressions
explain how to determine if the two expressions are equivalent using x = 6 and x = 10.
8x + 40
8(x + 5)

Explanation:

Step1: Substitute \( x = 6 \) into both expressions

For \( 8x + 40 \): \( 8(6) + 40 = 48 + 40 = 88 \)
For \( 8(x + 5) \): \( 8(6 + 5) = 8(11) = 88 \)

Step2: Substitute \( x = 10 \) into both expressions

For \( 8x + 40 \): \( 8(10) + 40 = 80 + 40 = 120 \)
For \( 8(x + 5) \): \( 8(10 + 5) = 8(15) = 120 \)

Step3: Compare the results

When \( x = 6 \), both expressions equal 88. When \( x = 10 \), both equal 120. Since the values match for both substitutions, the expressions are equivalent.

Answer:

The two expressions \( 8x + 40 \) and \( 8(x + 5) \) are equivalent because substituting \( x = 6 \) and \( x = 10 \) into both gives the same results (88 and 120, respectively).