Question

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

Four minus 7 times a number is equal to 12 minus 3 times the number.

Short answer

The required equation is $4-7x=12-3x$ and the solution is $x=-2$

Step-by-step solution

Step-1 – Given

Four minus 7 times a number is equal to 12 minus three times a 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, four minus 7 times a number = $4-7x$

12 minus three times a number = $12-3x$

According to the question $4-7x=12-3x$

Now we solve the equation,

$\begin{array}{l}4-7x=12-3x\text{Writetheoriginalequation}\\ 4-7x+3x=12-3x+3x\text{Add}3x\text{tobothsides}\\ 4-4x=12\text{Simplify}\\ 4-12-4x=12-12\text{Subtract12frombothsides}\\ -8-4x=0\text{Simplify}\\ -8-4x+8=0+8\text{Add8tobothside}\\ -4x=8\text{Simplify}\\ \frac{-4x}{-4}=\frac{8}{-4}\text{Divideeachside}\left(-\text{4}\right)\\ x=-2\text{Simplify}\end{array}$

Therefore, the solution of the equation $4-7x=12-3x$ is $x=-2$