If you would like to practice solving one-variable equations before continuing this lesson, use the applet below to work through some practice problems. Click on the image to access the applet.You may have studied ways to solve one-variable equations using algebra tiles and symbolic methods.
If you would like to practice solving one-variable equations before continuing this lesson, use the applet below to work through some practice problems. Click on the image to access the applet.
Let’s practice how you can apply properties of real numbers, including the commutative property, the associative property, and the distributive property, to solve an inequality that is written in symbolic form. For inequalities, properties of algebra apply just like they do with equations.
Anja wants to solve the inequality 6.5(x – 4) > 22.75 using the properties of real numbers. In the interactive below, drag the steps that Anja might use into the correct order by clicking and dragging on the tile from the "Symbolic Steps" box. Identify the property of real numbers that justifies why Anja can do that step with the symbolic representation of the inequality by clicking and dragging on the tile from the "Properties" box. You may use some properties more than once or not at all.
When solving an inequality where you have multiplied or divided by a negative number, you have to make sure that the inequality symbol still creates a true statement.
On your own paper, complete the table below, including the appropriate inequality symbol. The first row has been completed for you.
Scroll over the table to check your answers.
What happens to the inequality symbol when a and b are multiplied by -1?
Interactive popup. Assistance may be required. The inequality symbol is reversed.
Whenever a linear inequality is multiplied or divided by a negative number, the inequality symbol must be reversed in order to preserve the value of the inequality.
Solve each of the inequalities below for the variable in the inequality.
Interactive popup. Assistance may be required.
When you divide by the coefficient of x, are you dividing by a negative number? If so, you will need to reverse the inequality symbol.
Interactive popup. Assistance may be required.
x < 13.6
Interactive popup. Assistance may be required.
When you divide by the coefficient of a, are you dividing by a negative number? If so, you will need to reverse the inequality symbol.
Interactive popup. Assistance may be required.
a ≤ -1
Interactive popup. Assistance may be required.
When you divide by the coefficient of m, are you dividing by a negative number? If so, you will need to reverse the inequality symbol.
Interactive popup. Assistance may be required.
m ≤ 14 over 3
14
3
Interactive popup. Assistance may be required.
When you divide by the coefficient of k, are you dividing by a negative number? If so, you will need to reverse the inequality symbol.
Interactive popup. Assistance may be required.
k < 7