Explain how solving a linear inequality is similar to solving a linear equation.

Question

Explain how solving a linear inequality is similar to solving a linear equation.

Choose the correct answer below.

A. The steps for solving a linear inequality are identical to the steps for solving a linear equation except when multiplication or division by a negative number happens.

B. If the inequality symbol is replaced by the equal​ sign, the solution set does not change.

C. The steps for solving a linear inequality are identical to the steps for solving a linear equation

Answer 1

In order to answer this question, we first need to understand how to solve linear equations and linear inequalities.

Let's start with an example of a linear equation:

3x - 5y = 10

-3x -3x

-5y = 10 - 3x

/-5 /-5 /-5

y = -2 + 3/5x

Now, what would happen if instead of an equation, that problem was a linear inequality?

3x - 5y <= 10

-3x -3x

-5y <= 10 - 3x

/-5 /-5 /-5

**Note** since we divide by -5 here, we must flip the sign of the inequality

y >= -2 +3/5x

Now that we've gone through examples, let's look back at our answer choices.

For C, the steps aren't exactly identical-- we had to flip the sign when solving the linear inequality, something that wasn't necessary when solving the linear equation.

For B, the solution set of the linear inequality and the equation are different. For example, (0,0) is a solution of the inequality, but not the equation.

That leaves us with answer A-- that the steps for solving the inequality and the equation were almost the same, except we flipped the inequality when dividing by a negative number.