Question

Select all expressions that represent a correct solution to the equation 6(x+4)=20. copied for free from openupresources.Org Select all that apply: A. (20−4)÷6 B. 16(20−4) C. 20−6−4 D. 20÷6−4 E. 1/6(20−24) F. (20−24)÷6

Answer 1

Option D: $20 \div 6-4$ is the correct solution to the equation $6(x+4)=20$

Option E: $\frac{1}{6} (20-24)$ is the correct solution to the equation $6(x+4)=20$

Option F: $(20-24) \div 6$ is the correct solution to the equation $6(x+4)=20$

Explanation:

The expression is $6(x+4)=20$

Let us find the value of x.

$\begin{aligned}6(x+4) &=20 \\6 x+24 &=20 \\6 x &=-4 \\x &=-\frac{2}{3}\end{aligned}$

Now, we shall find the expression that is equivalent to the value $x=-\frac{2}{3}$

Option A: $(20-4) \div 6$

Simplifying the expression, we have,

$\frac{16}{6}=\frac{8}{3}$

Since, $\frac{8}{3}$ is not equivalent to $x=-\frac{2}{3}$, the expression $(20-4) \div 6$ is not equivalent to the equation $6(x+4)=20$

Hence, Option A is not the correct answer.

Option B: $16(20-4)$

Simplifying the expression, we have,

$16(16)=256$

Since, 256 is not equivalent to $x=-\frac{2}{3}$, the expression $16(20-4)$ is not equivalent to the equation $6(x+4)=20$

Hence, Option B is not the correct answer.

Option C: $20-6-4$

Simplifying the expression, we have,

$20-10=10$

Since, 10 is not equivalent to $x=-\frac{2}{3}$, the expression $20-6-4$ is not equivalent to the equation $6(x+4)=20$

Hence, Option C is not the correct answer.

Option D: $20 \div 6-4$

Using PEMDAS and simplifying the expression, we have,

$\begin{aligned}(20 \div 6)-4 &=\frac{10}{3}-4 \\ &=\frac{10-12}{3} \\ &=-\frac{2}{3} \end{aligned}$

Thus, $-\frac{2}{3}$ is equivalent to $x=-\frac{2}{3}$, the expression $20 \div 6-4$ is equivalent to the equation $6(x+4)=20$

Hence, Option D is the correct answer.

Option E: $\frac{1}{6} (20-24)$

Simplifying the expression, we have,

$\begin{aligned} \frac{1}{6}(20-24) &=\frac{1}{6}(-4) \\ &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$

Thus, $-\frac{2}{3}$ is equivalent to $x=-\frac{2}{3}$, the expression $\frac{1}{6} (20-24)$ is equivalent to the equation $6(x+4)=20$

Hence, Option E is the correct answer.

Option F: $(20-24) \div 6$

Simplifying the expression, we have,

$\begin{aligned}(20-24) \div 6 &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$

Thus, $-\frac{2}{3}$ is equivalent to $x=-\frac{2}{3}$, the expression $(20-24) \div 6$ is equivalent to the equation $6(x+4)=20$

Hence, Option F is the correct answer.