Question

4 select all expressions that represent a correct solution to the equation $6(x + 4) = 20$.
a. $(20 - 4) \div 6$
b. $\frac{1}{6}(20 - 4)$
c. $20 - 6 - 4$
d. $20 \div 6 - 4$
e. $\frac{1}{6}(20 - 24)$
f. $(20 - 24) \div 6$

Explanation:

Step1: Solve for x via division

Divide both sides by 6:
$\frac{6(x+4)}{6} = \frac{20}{6}$
Simplify to get: $x + 4 = \frac{20}{6}$

Step2: Isolate x by subtracting 4

Subtract 4 from both sides:
$x = \frac{20}{6} - 4$

Step3: Rewrite using distributive property

Start with original equation, expand left side:
$6x + 24 = 20$
Rearrange to isolate $6x$:
$6x = 20 - 24$
Divide by 6: $x = \frac{20 - 24}{6}$

Step4: Verify equivalent forms

$\frac{20}{6} - 4$ matches option D. $\frac{20 - 24}{6}$ is equivalent to $\frac{1}{6}(20 - 24)$ (matches E) and $(20 - 24) \div 6$ (matches F).

Answer:

D. $20 \div 6 - 4$
E. $\frac{1}{6}(20 - 24)$
F. $(20 - 24) \div 6$