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Chapter 6: Problem 21

Solve and check each equation. \(9(5 x-2)=45\)

Short Answer

Expert verified
The solution is \(x = \frac{7}{5}\).

Step by step solution

01

Apply the distributive property

Multiply 9 by each term inside the parentheses to simplify the equation. So, the equation becomes \(45 x - 18 = 45\).
02

Isolate the variable

To do this, add 18 on both sides of the equation to cancel out -18 on the left side of the equation. Now the equation becomes \( 45 x = 63 \).
03

Solve for x

To isolate x, we need to divide both sides of the equation by 45. So \( x = \frac{63}{45} \).
04

Simplify the fraction

Simplify the fraction to have it in the lowest terms. Therefore \( x = \frac{7}{5} \).
05

Check the solution

To check, substitute \(x = \frac{7}{5}\) back into the original equation \(9(5x-2)=45\). If the left side equals to the right side, then the solution is correct.

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