Solve the absolute value equations. -1=-|5 x+7|

Name: Problem 32, Chapter 1: Intermediate Algebra
Uploaded: 2020-06-15T09:56:56-08:00
Duration: 1 min 30 s
Channel: Ankit Gupta
Description: Solve the absolute value equations. -1=-|5 x+7|

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Key Concepts

Algebraic Manipulation in Equations

Algebraic manipulation is an essential technique when solving equations, including those with absolute values. This consists of performing operations such as multiplying or adding the same value to both sides of an equation to isolate the variable or expression of interest, while attentively preserving the equality. Special care should be taken when negative signs are involved to avoid incorrect conclusions.

Absolute Value Equations

Solving equations that involve absolute values typically requires setting up multiple cases to account for the two possible scenarios that satisfy the absolute value operation. This often involves isolating the absolute value expression and then considering both the positive and negative possibilities of the expression inside the absolute value.

Absolute Value Function

The absolute value function measures the distance of a number from zero on the number line, and it always returns a nonnegative result. This core property means that any expression inside the absolute value will yield a zero or positive output, regardless of whether the original expression is positive or negative.

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