Solve each equation and inequality. For the inequalities, graph the solution set and write it us

step 1 Got a fun absolute value equation we're going to solve here. 11 .12 equals the absolute value of

Solve each equation and inequality. For the inequalities,...

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Key Concepts

Simplifying Rational Expressions

Simplifying rational expressions is the process of manipulating fractions to combine like terms, find a common denominator, and reduce the expression to a simpler form. This technique is important when solving algebraic equations, as it allows for the isolation of variables and makes the computations more straightforward.

Case Analysis

When solving equations that contain an absolute value, it is necessary to perform case analysis. This means setting up two separate equations: one in which the expression inside the absolute value is equal to the positive value, and one in which it is equal to the negative value. This systematic approach ensures that all possible solutions to the equation are identified.

Absolute Value Equations

Absolute value equations involve expressions inside an absolute value operator being set equal to some quantity. Since the absolute value of a number represents its distance from zero, such equations require considering the situation where the expression inside the absolute value is both positive and negative. This principle is central to solving any equation that features an absolute value term.

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