Chapter 1.2, Problem 34E

To determine

To solve: Write and solve the equation to find the number.

Answer to Problem 34E

The required number is 10.

Explanation of Solution

Given information:

Four times the difference of a number and 7 is 12.

Calculation:

Let unknown number be = $x$

According to the question ,

Difference of a number x and 7 = $\left(x-7\right)$

Four times the difference of a number and 7 = $4\left(x-7\right).$

Therefore, given statement “Four times the difference of a number and 7 is 12” could be represented as

  $4\left(x-7\right)=12$

Now, we need to simplify above equation.

  $4\left(x-7\right)=12$

Distribute 4 over ( x -7)

  $4x-28=12$

Add 28 on both side of the equation

  $4x-28+28=12+28$

  $\Rightarrow 4x=40$

Divide both sides by 4

  $\frac{4x}{4}=\frac{40}{4}$

  $x=10$

Therefore, the number is10.