Q14. - Algebra 1

Question

Write an equation and solve each problem. 

Three less than three fourths of a number is negative 9. Find the number.

Step-by-Step Solution

Answer

$\frac{3}{4}x-3=-9$

and

$x=-8$

Step 1. Given Statement.

Three less than three fourths of a number is negative 9.

Step 2. Description of step.

In order to solve the given problem, first convert the statement into an equation.

For this, let the unknown number in the equation be x 

Then, three fourths of that number is $\frac{3}{4}x$, and three less than three fourths of a number is negative 9 is represented by the equation:

$\frac{3}{4}x-3=-9$

Now find the value of unknown by solving above equation, as:

$\begin{array}{c}\frac{3}{4}x-3=-9\\ \frac{3}{4}x=-9+3\\ \frac{3}{4}x=-6\\ \frac{3}{4}x\times \frac{4}{3}=-6\times \frac{4}{3}\\ x\times \frac{3}{4}\times \frac{4}{3}=-2\times 4\\ x\times 1=-8\\ x=-8\end{array}$ 

Thus, the unknown number is $x=-8$.