Problem 87 - College Algebra Essentials

Question

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

The resulting statement is true.

Step 1: Substitute 6 for x

The first step is to substitute the value 6 for x in the given equation, which leads to: \[ 2*(6-3)-17 = 13 - 3*(6+2) \]

Step 2: Simplify both sides

After substitution, simplify the equation by doing the addition, subtraction, and multiplication operations. The left side simplifies to (2*3)-17, and the right side simplifies to 13-(3*8). The equation becomes: \[ 2*3 - 17 = 13 - 3*8 \]

Step 3: Evaluate the expressions

Now, evaluate the expressions on both sides of the equation. The left side evaluates to 6-17 = -11 and the right side evaluates to 13-24 = -11.

Step 4: Comparison

By comparing both sides, it is seen that both sides are equal resulting in a true statement.