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Chapter 1: Problem 87

This will help you prepare for the material covered in the next section. If 6 is substituted for \(x\) in the equation $$2(x-3)-17=13-3(x+2)$$ is the resulting statement true or false?

Short Answer

Expert verified
After replacing \(x\) with 6 in the given equation, the resultant statement is true.

Step by step solution

01

Substitute the given value into the equation

Replace \(x\) in the given equation \(2(x-3)-17=13-3(x+2)\) with 6: \(2(6-3)-17=13-3(6+2)\)
02

Simplify the Brackets

Perform the subtraction inside the brackets:\(2(3)-17=13-3(8)\)
03

Apply the Multiplication

Multiply the numbers outside the brackets with the result of subtraction inside the brackets:\(6-17=13-24\)
04

Perform the Subtraction

Perform the subtraction operation:\(-11=-11\)
05

Check the truthfulness of the resulting statement

As we see, both sides of the equation are equal. Thus, after substituting 6 for \(x\), the resulting statement is true

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Most popular questions from this chapter

Use the graph of \(y-|4-x|\) to solve each inequality. \(|4-x| \geq 5\)

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Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(7-\frac{4}{5} x<\frac{3}{5}\)

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