Problem 155 - College Algebra Essentials

Question

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$x-0.02(x+200)=0.98 x-4$$

Step-by-Step Solution

Answer

The initial statement is false. The true statements would be \(0.98x + 4 = 4\) or \(0.98x - 4 = -4\).

Step 1: Distribute

Start this problem by distributing the 0.02, so the equation becomes \(0.98x + 4 = 0.98x - 4\).

Step 2: Simplify

Simplify the equation by subtracting 0.98x from both sides. This leads to: \(4 = -4\).

Step 3: Test the truth of the statement

This is clearly not a true statement. 4 and -4 are not equal in value.

Step 4: Make the necessary changes to produce a true statement

To make a true statement, either change the right hand side to 4 or change the left hand side to -4. So the equation could be \(0.98x + 4 = 4\) or the equation could be \(0.98x - 4 = -4\).