Problem 136 - College Algebra

Question

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

Step-by-Step Solution

Answer

The main differences in solving linear inequalities versus linear equations are that when a linear inequality is multiplied or divided by a negative number you must reverse the inequality sign and a linear inequality's solution is a range of values while a linear equation has a specific solution.

Step 1: Understand the differences in the problem

A linear equation is an equation that may be put into the form a*x = b, where a and b are constants. It is solved by isolating the variable on one side of the equation. A linear inequality, on the other hand, can be put in the form a*x > b or a*x < b. The goal with an inequality is to find a range of possible solutions, rather than one specific solution.

Step 2: Explore the differences in solving the problems

When solving a linear equation, steps that involve adding, subtracting, multiplying, or dividing terms on both sides do not change the equality. However, when dealing with a linear inequality, if you are to multiply or divide both side by a negative number, the sign of the inequality flips. That is, '>' becomes '<' and vice versa.

Step 3: Discuss Result Presentation

The solution of a linear equation is typically a single real number whereas the solution to an inequality is not a single value but a range of values expressed as an interval. The solution to a linear inequality is expressed using inequality notation or interval notation or a graph on a number line, while the solution to a linear equation is typically represented by a single value.