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Chapter 0: Problem 155

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

Short Answer

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

Step by step solution

01

Distribute

Start this problem by distributing the 0.02, so the equation becomes \(0.98x + 4 = 0.98x - 4\).
02

Simplify

Simplify the equation by subtracting 0.98x from both sides. This leads to: \(4 = -4\).
03

Test the truth of the statement

This is clearly not a true statement. 4 and -4 are not equal in value.
04

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 \(0.98x - 4 = -4\).

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