Question

7 decide if each pair of expressions is equivalent. choose yes or no for each statement.
a. $6(-5a + 4)$ and $3(-10a + 8)$
b. $\frac{1}{6}(15a - 36)$ and $\frac{1}{2}a - (3a + 6)$
c. $-3a + 1.5$ and $-0.5(6a + 1.5)$
d. $-4(a - 4 + 2a + 8)$ and $-4(a - 4) - 4(2a + 8)$

Explanation:

Step1: Expand first expression (a)

$6(-5a + 4) = -30a + 24$

Step2: Expand second expression (a)

$3(-10a + 8) = -30a + 24$

Step3: Expand first expression (b)

$\frac{1}{6}(15a - 36) = \frac{15}{6}a - \frac{36}{6} = 2.5a - 6$

Step4: Simplify second expression (b)

$\frac{1}{2}a - (3a + 6) = 0.5a - 3a - 6 = -2.5a - 6$

Step5: Expand first expression (c)

$-3a + 1.5$ (already simplified)

Step6: Expand second expression (c)

$-0.5(6a + 1.5) = -3a - 0.75$

Step7: Simplify first expression (d)

$-4(a - 4 + 2a + 8) = -4(3a + 4) = -12a - 16$

Step8: Expand second expression (d)

$-4(a - 4) - 4(2a + 8) = -4a + 16 - 8a - 32 = -12a - 16$

Answer:

a. Yes
b. No
c. No
d. Yes