Question

Solve the equation. $$|5-4 x|-3=4$$

   Solve the equation.
$$|5-4 x|-3=4$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 6, Problem 34

Instant Answer

Solved by Expert Suman Saurav Thakur

09/04/2020

Step 1

Step 1: First, we add 3 to both sides of the equation to isolate the absolute value: $$|5-4x|=4+3$$ This simplifies to: $$|5-4x|=7$$ Show more…

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Solve the equation. $$|5-4 x|-3=4$$

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Key Concepts

Algebraic Manipulation

Solving equations with absolute value expressions also involves algebraic techniques such as isolating the absolute value expression, adding or subtracting constants from both sides, and then solving the resulting linear equations. This process is key to reducing the equation to a solvable form after applying the case analysis.

Absolute Value Function

The absolute value function, denoted by |x|, outputs the non-negative value of any real number, meaning that |x| equals x if x is positive or zero and -x if x is negative. This concept is central to solving equations where the variable is within an absolute value expression.

Case Analysis

When working with absolute value equations, it is important to use case analysis. This involves splitting the equation into separate cases based on the sign of the expression inside the absolute value, and then solving each case individually to ensure all possible solutions are considered.

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