Question

Write the verbal sentence as an equation. Then solve the equation.

Twelve less than -9 times a number is equal to 8 minus 4 times the number.

Short answer

The required equation is $-9x-12=8-4x$ and the solution is $x=-4$

Step-by-step solution

Step-1 – Given

12 less than $-9$ times a number is equal to 8 minus 4 times the number.

Step-2 – To determine

We have to write the equation by writing verbal sentence as equation. Then we solve the equation.

Step-3 – Calculation

Let the unknown number is x

So, 12 less than $-9$times a number = $-9x-12$

8 minus 4 times the number = $8-4x$

According to the question $-9x-12=8-4x$

Now we solve the equation,

$\begin{array}{l}-9x-12=8-4x\text{writetheoriginalequation}\\ -9x+4x-12=8-4x+4x\text{add}4x\text{tobothsides}\\ -5x-12=8\text{simplify}\\ -5x-12-8=8-8\text{subtract8frombothsides}\\ -5x-20=0\text{simplify}\\ -5x=20\\ \frac{-5x}{-5}=\frac{20}{-5}\text{divideeachsideby}-5\\ x=-4\text{simplify}\end{array}$

Therefore, the solution of the equation $-9x-12=8-4x$ is $x=-4$