Question

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

Three less than 11 times a number is equal to 9 plus 5 times the number.

Short answer

The required equation is $11x-3=9+5x$ and the solution is $x=2$

Step-by-step solution

Step-1 – Given

Three less than 11 times a number is equal to 9 plus 5 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, three less than 11 times a number = $11x-3$

9 plus 5 times the number = $9+5x$

According to the question $11x-3=9+5x$

Now we solve the equation,

$\begin{array}{l}11x-3=9+5x\text{writetheoriginalequation}\\ 11x-3+3=9+3+5x\text{add3tobothsides}\\ 11x=12+5x\text{simplify}\\ 11x-5x=12+5x-5x\text{subtract}5x\text{frombothsides}\\ 6x=12\text{simplify}\\ \frac{6x}{6}=\frac{12}{6}\text{divideeachsideby6}\\ x=2\text{simplify}\end{array}$

Therefore, the solution of the equation $11x-3=9+5x$ is $x=2$