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Chapter 6: Problem 27

Solve and check each equation. \(8 x-2=7 x-5\)

Short Answer

Expert verified
The solution to the equation \(8x - 2 = 7x - 5\) is \(x = -3\).

Step by step solution

01

Isolate variables

Subtract \(7x\) from both sides of the given equation \(8x - 2 = 7x - 5\) to get \(x - 2 = -5\). This is accomplished using the property of equality which allows the subtraction of the same value from both sides.
02

Further isolate 'x'

Next, get 'x' alone by adding 2 to both sides of the equation \(x - 2 = -5\), resulting in \(x = -3\). This is adding 2 to both sides of the equation, using the property of equality which allows adding the same value to both sides.
03

Verify solution

The validity of the obtained solution can be checked by substituting \(x = -3\) back into the original equation: \(8(-3) - 2 =? 7(-3) - 5\). When simplified, both sides yield -26, confirming that \(x = -3\) is indeed the solution to the given equation.

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Most popular questions from this chapter

Solve: \(x^{2}+2 \sqrt{3} x-9=0\).

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