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Absolute Value Equations

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Questions and Answers

What is the first step in solving an absolute value equation?

Divide both sides by a constant

Add or subtract a constant from both sides (correct)

Solve for the variable

Apply the absolute value rule

What is the result of the equation $5|4x-3| = 20$ after isolating the absolute value?

$|4x-3| = 4$ (correct)

$|4x-3| = 2$

$|4x-3| = 20$

$|4x-3| = 5$

What are the two cases we solve for after applying the absolute value rule to $|4x-3| = 4$?

$4x+3 = 4$ or $4x+3 = -4$

$4x-3 = 4$ or $4x-3 = -4$ (correct)

$4x+3 = 4$ or $4x-3 = -4$

$4x-3 = 4$ or $4x+3 = -4$

What are the solutions to the equations $4x-3 = 4$ and $4x-3 = -4$?

<p>$x=7/4$ and $x=-1/4$</p> Signup and view all the answers

What is the purpose of checking for extraneous solutions when solving an absolute value equation?

<p>To ensure the solutions satisfy the original equation</p> Signup and view all the answers

Study Notes

Solving Absolute Value Equations: The First Step

Isolate the absolute value expression. This means getting the expression containing the absolute value symbol by itself on one side of the equation.

Isolating the Absolute Value

For the equation 5|4x - 3| = 20, isolating the absolute value results in |4x - 3| = 4.

Applying the Absolute Value Rule

After isolating the absolute value, we solve two separate equations:
- Case 1: 4x - 3 = 4
- Case 2: 4x - 3 = -4

Solving the Equations

The solution to 4x - 3 = 4 is x = 7/4.
The solution to 4x - 3 = -4 is x = -1/4.

Checking for Extraneous Solutions

Checking for extraneous solutions is crucial because operations performed during the solving process might introduce solutions that don't satisfy the original equation. Extraneous solutions must be rejected.

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Description

Solve Absolute Value Equations: Test your skills in solving equations involving absolute value by following step-by-step instructions. Practice isolating the absolute value, applying the two cases rule, and simplifying to find the solution. Take this quiz to enhance your equation-solving abilities!