Q24. - Algebra 1

Question

Write an equation and solve each problem.

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

Step-by-Step Solution

Answer

The required number is 8.

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.