Solve each equation or inequality.∣x+10∣=∣x−11∣|x+10| = |x-11|

Ch. 1 - Equations and Inequalities

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

All textbooks

Lial 13th Edition

Ch. 1 - Equations and Inequalities

Problem 112

Chapter 2, Problem 112

Solve each equation or inequality.
$∣ x + 10 ∣ = ∣ x - 11 ∣$

Verified step by step guidance

Recognize that the equation involves absolute values: $|x+10| = |x-11|$. The absolute value of a number represents its distance from zero on the number line, so this equation states that the distance of $x+10$ from zero is equal to the distance of $x-11$ from zero.

Set up two cases to solve the equation, because absolute value equations can be split into cases where the expressions inside the absolute values are either equal or opposites:

Case 1: $x + 10 = x - 11$

Case 2: $x + 10 = -(x - 11)$

Solve each case separately by simplifying and isolating $x$ to find the possible solutions.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Absolute Value Definition

The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. For any real number x, |x| equals x if x is non-negative, and -x if x is negative. Understanding this helps in rewriting and solving equations involving absolute values.

Solving Absolute Value Equations

Equations involving absolute values can be solved by considering the definition of absolute value, leading to two cases: one where the expressions inside the absolute values are equal, and one where they are opposites. This approach allows breaking down the equation into simpler linear equations.

Properties of Equality and Inequality

When solving equations, properties of equality allow manipulation of both sides to isolate variables. For absolute value equations, setting the expressions inside equal or opposite requires careful application of these properties to find all possible solutions.

Recommended video: