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Chapter 6: Problem 39

Solve and check each equation. \(5(2 x-8)-2=5(x-3)+3\)

Short Answer

Expert verified
The solution to the equation is \(x = 6\).

Step by step solution

01

Distribute the multiplication across the brackets

Begin by distributing in the equation: \(5(2x-8)-2=5(x-3)+3\). This yields: \(10x - 40 - 2 = 5x - 15 + 3\)
02

Simplify both sides of the equation

Next, simplify both sides of the equation: \(10x - 42 = 5x - 12\)
03

Move terms with x to one side and constants to the other side

Move the \(x\) terms to one side of the equation and constants to the other side. This gives: \(10x - 5x = -12 + 42\)
04

Solve for x

Continue to solve for \(x\) by simplifying the equation: \(5x = 30\). Therefore, \(x = 30/5 = 6\)
05

Check the found solution

Substitute \(x=6\) back into the original equation to verify the solution. Upon substitution we see that both sides are equal, hence confirming that the solution is correct.

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