Problem 135 - College Algebra

Question

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

Step-by-Step Solution

Answer

Both solving a linear equation and inequality involve isolating the variable on one side and using the same set of arithmetic operations. The main difference is in the nature of the solutions; an equation has a single value solution whereas an inequality has a range of possible solutions.

Step 1: Solving a linear equation

The process of solving a linear equation involves isolating the variable on one side of the equation by using operations such as addition, subtraction, multiplication, and division. This is done to see what value (or range of values) of the variable makes the equation true.

Step 2: Solving a linear inequality

Solving a linear inequality also involves isolating the variable, similar to a linear equation. However, unlike an equation, an inequality does not have a singular solution but a range of solutions. Operations such as addition, subtraction, multiplication, and division can be used, but we should remember that if you multiply or divide by a negative number, the direction of the inequality sign must be reversed.

Step 3: Similarities

So, both processes involve isolating the variable through similar mathematical operations. The goal in each case is finding values for the variable which would satisfy the condition (equality or inequality). One key difference is that the solution for a linear equation would be a single value whereas the solution for a linear inequality would be a range of values.