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Chapter 6: Problem 97

Describe ways in which solving a linear inequality is similar to solving a linear equation.

Short Answer

Expert verified
Solving a linear equation and a linear inequality both involve isolating the variable, and applying the same operations to both sides of the equation or inequality. However, unlike in equations, the inequality sign flips when both sides are divided or multiplied by a negative number. Furthermore, solutions to inequalities can be ranges of numbers instead of single values.

Step by step solution

01

Identifying similarities

In both processes, one tries to isolate the variable for which the solution is sought. For example, if working with a problem like 'x+3 = 5' or 'x+3 > 5', in both cases the goal is to leave 'x' on one side of the equality or inequality.
02

Applying the same operations to both sides

Just like with linear equations, in linear inequalities, whatever operation is performed on one side, the same needs to be done to the other side. This balance is maintained to ensure the inequality/equality continues to be true.
03

Rule for multiplying or dividing by negative numbers

There is one critical exception: When multiplying or dividing by a negative number when dealing with inequalities, the inequality sign is flipped. So if we have '-x < 5', and we divide both sides by -1, the resulting inequality is 'x > -5'.
04

Multiple solutions

Unlike equations, inequalities can have multiple solutions. For example, if 'x > 3', 'x' can be any number greater than 3, therefore the 'solution' is a range of numbers.

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Most popular questions from this chapter

Use FOIL to find the products. \((3 x-7)(4 x-5)\)

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