Problem 154 - 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. $$-x-x=-x+(-x)=0$$

Step-by-Step Solution

Answer

The first part of the statement '-x - x = -x + (-x)' is true. The second part '-x + (-x) = 0' is only true when 'x' is 0.

Step 1: Analysis of the Equation

The equation '-x - x = -x + (-x) = 0' can be broken down into two sub-statements: '-x - x = -x + (-x)' and '-x + (-x) = 0'.

Step 2: Verification of the First Sub-statement

First, let's simplify the expressions on both sides of the first sub-statement. '-x - x' simplifies to '-2x', and '-x + (-x)' also simplifies to '-2x'. Hence, '-2x = -2x' is valid.

Step 3: Verification of the Second Sub-statement

Next, consider the second sub-statement '-x + (-x) = 0'. This simplifies to '-2x = 0'. This statement is valid only if x=0. If x was any other number, the statement would be false.