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Chapter 1: Problem 87

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
The resulting statement is true.

Step by step solution

01

Substitute for \(x\)

Begin by substituting the value \(x = 6\) into the equation. It becomes: \(2(6-3)-17=13-3(6+2)\)
02

Simplify the equation

Next, do the arithmetic within the parenthesis first (according to order of operations), then follow through with the multiplication and subtraction: So the equation simplifies to: \[2(3) - 17 = 13 -3(8)\] \[6 -17 = 13 - 24\] \[-11 = -11\]
03

Compare both sides

Finally, examine the simplified statement. Both sides of the equation equal to \(-11\), which means the original statement is true when \(x = 6\).

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Most popular questions from this chapter

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