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Chapter 0: Problem 126

Describe ways in which solving a linear inequality is different than solving a linear equation.

Short Answer

Expert verified
Three key differences between solving a linear equation and a linear inequality include: 1) The solution set of an inequality is a range of values, while an equation has specific solutions. 2) When multiplying or dividing an inequality by a negative number, the direction of the inequality changes. 3) Solutions to an inequality can be graphically represented on a number line.

Step by step solution

01

Differences in Solution Set

One of the largest differences between solving linear equations and inequalities is in the solution set. In solving a linear equation, the solution is a certain value(s) whereas for a linear inequality, the solution includes an array of values which are often expressed in terms of a range or interval.
02

Applying Operations

In general, the operations used while solving both equations and inequalities are same. You can add, subtract, multiply or divide any value from both sides. However, there is a key distinction when it comes to multiplying or dividing by negative numbers in case of inequalities. When you multiply or divide both sides of an inequality with a negative number, you must flip the inequality symbol.
03

Graphical Representation

The solutions to a linear inequality can be represented graphically on a number line which is not the case with a linear equation. In fact, a strict inequality (greater than, less than) will be represented with an open circle on the number line, and a non-strict inequality (greater than equal to, less than equal to) is represented by a filled in circle. In this way, solving a linear inequality provides a visual component that is not typically present with linear equations.

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