Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is larger or smaller than the other.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

Front

What is the solution to the inequality -2x + 3(-4x + 6) ≤ 116?

Back

x ≥ -7

Front

What is the solution to the inequality 15 + 7x ≥ 29?

Back

x ≥ 2

Front

What is the solution to the inequality 4x - 3 < -1x + 12?

Back

x < 3

Front

When solving inequalities, does the sign need to flip when multiplying or dividing by a negative number?

Back

Yes, the sign must flip when multiplying or dividing both sides of an inequality by a negative number.

Front

What is the solution to the inequality -2x + 2 > 3x - 8?

Back

x < 2

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left can be greater than or equal to the value on the right.

Front

How do you graph the solution of an inequality on a number line?

Back

To graph an inequality, use an open circle for < or > (not including the endpoint) and a closed circle for ≤ or ≥ (including the endpoint). Shade the region that represents the solution.