Question

Write an equation and solve each problem.

Fourteen less than three fourths of a number is negative eight. Find the number.

Short answer

The required number is 8.

Step-by-step solution

Step 1. List the given data.

Fourteen less than three fourths of a number is negative eight.

Step 2. Write the equation for the given problem.

Let $x$be the required number.

Translating the given problem into equation form,

$\frac{3}{4}x-14=-8$

This is the required equation for the given problem.

Step 3. Solve the equation.

Solving,

$\frac{3}{4}x-14=-8$ (Obtained equation)

$\frac{3}{4}x-14+14=-8+14$ (Add 14 to both sides)

$\frac{3}{4}x=6$ (Simplify)

$\frac{3}{4}x\times \frac{4}{3}=6\times \frac{4}{3}$ (Multiply both sides by $\frac{4}{3}$)

$x=8$ (Simplify)

So, $x=8$is the solution of the obtained equation.

Step 4. Interpret the obtained solution.

According to the assumption, $x$is the required number which satisfies the given problem.

Thus, the required number is 8.