Problem 87 - College Algebra

Question

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?

Step-by-Step Solution

Answer

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

Step 1: Substitute the given value into the equation

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

Step 2: Simplify the Brackets

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

Step 3: Apply the Multiplication

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

Step 4: Perform the Subtraction

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

Step 5: 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