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Q25.

Expert-verified
Found in: Page 133

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Write the verbal sentence as an equation. Then solve the equation.Four minus 7 times a number is equal to 12 minus 3 times the number.

The required equation is $4-7x=12-3x$ and the solution is $x=-2$

See the step by step solution

## Step-1 – Given

Four minus 7 times a number is equal to 12 minus three times a 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, four minus 7 times a number = $4-7x$

12 minus three times a number = $12-3x\text{}$

According to the question $4-7x=12-3x\text{}$

Now we solve the equation,

$\begin{array}{l}4-7x=12-3x\text{Write the original equation}\\ 4-7x+3x=12-3x+3x\text{Add}3x\text{to both sides}\\ 4-4x=12\text{Simplify}\\ 4-12-4x=12-12\text{Subtract 12 from both sides}\\ -8-4x=0\text{Simplify}\\ -8-4x+8=0+8\text{Add 8 to both side}\\ -4x=8\text{Simplify}\\ \frac{-4x}{-4}=\frac{8}{-4}\text{Divide each side}\left(-\text{4}\right)\\ x=-2\text{Simplify}\end{array}$

Therefore, the solution of the equation $4-7x=12-3x\text{}$ is $x=-2\text{}$