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First, isolate the absolute value expression.

Linear Absolute Value Equation: Solving Algebraically

Example 1: Solve .08152 x

8152 x

415 x

415415 xorx

Next, examine the constant on the right side. If it is positive proceed as follows. Write two new equations. Form one by dropping the absolute value bars. Form the other by dropping the absolute value bars and changing the sign of the constant term. Place the word "or" between these statements.

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Linear Absolute Value Equation: Solving Algebraically

Slide 2

Now solve each equation. The "or" means that the solution of each equation is a solution of the original equation.

5535 xorx

153 xorx

See next slide for notes.

415415 xorx

The solution set is .53

,1

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Linear Absolute Value Equation: Solving Algebraically

Slide 3

If after isolating the absolute value expression, the constant term on the right is negative, the equation would have no solution because any real number substituted for x would cause the absolute value expression to produce a nonnegative number.

If after isolating the absolute value expression, the constant term on the right is zero, remove the absolute value bars and solve the resulting equation. For example, solving |2x + 3| = 0 would result in solving 2x + 3 = 0.

Notes:

Table of Contents

Linear Absolute Value Equation: Solving Algebraically