Question

$\frac{2}{3}(6 - 9x) = 16$ a -2 b -4 c -9 d -12

Explanation:

Step1: Eliminate the fraction

Multiply both sides of the equation $\frac{2}{3}(6 - 9x)=16$ by $\frac{3}{2}$ to get rid of the fraction. So we have $6 - 9x = 16\times\frac{3}{2}$.
Calculate $16\times\frac{3}{2}=24$, so the equation becomes $6 - 9x = 24$.

Step2: Isolate the term with x

Subtract 6 from both sides: $-9x = 24 - 6$.
Calculate $24 - 6 = 18$, so $-9x = 18$.

Step3: Solve for x

Divide both sides by -9: $x=\frac{18}{-9}$.
Simplify to get $x = - 2$. Wait, but the highlighted option is B (-4). Wait, maybe I made a mistake. Let's check again.

Wait, original equation: $\frac{2}{3}(6 - 9x)=16$. Let's re - solve:

Multiply both sides by 3: $2(6 - 9x)=48$.

Expand the left side: $12-18x = 48$.

Subtract 12 from both sides: $-18x=48 - 12=36$.

Divide both sides by -18: $x=\frac{36}{-18}=-2$. Wait, but the highlighted option is B. Maybe there is a mistake in the problem or my calculation? Wait, no, let's check the options again.

Wait, maybe the original equation is $\frac{2}{3}(6 - 9x)= - 16$? Let's try that.

Multiply both sides by 3: $2(6 - 9x)=-48$.

Expand: $12-18x=-48$.

Subtract 12: $-18x=-60$.

Divide by -18: $x=\frac{-60}{-18}=\frac{10}{3}\approx3.33$, not matching.

Wait, maybe the equation is $\frac{2}{3}(6 + 9x)=16$?

Multiply by 3: $2(6 + 9x)=48$.

Expand: $12 + 18x = 48$.

Subtract 12: $18x = 36$.

Divide by 18: $x = 2$. No.

Wait, maybe the equation is $\frac{2}{3}( - 6 - 9x)=16$?

Multiply by 3: $2(-6 - 9x)=48$.

Expand: $-12-18x = 48$.

Add 12: $-18x=60$.

Divide by -18: $x=\frac{60}{-18}=-\frac{10}{3}\approx - 3.33$. No.

Wait, the highlighted option is B (-4). Let's plug x = - 4 into the original equation:

Left side: $\frac{2}{3}(6-9\times(-4))=\frac{2}{3}(6 + 36)=\frac{2}{3}\times42 = 28
eq16$.

Plug x=-2: $\frac{2}{3}(6-9\times(-2))=\frac{2}{3}(6 + 18)=\frac{2}{3}\times24 = 16$. So x=-2, which is option A. But the highlighted is B. Maybe a mistake in the problem's highlight. But according to the calculation, x=-2, so the correct answer should be A. -2. But the highlighted option in the picture is B. Maybe there is a typo in the problem.

Answer:

A. -2