Solving Multi-Step Inequalities Warm-up

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

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 set of an inequality?

Back

The solution set is the set of all values that satisfy the inequality.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable, perform inverse operations (addition, subtraction, multiplication, division) on both sides of the inequality.

Front

What is the first step in solving the inequality -p - 4p > -10?

Back

Combine like terms: -5p > -10.

Front

What is the final solution for the inequality -p - 4p > -10?

Back

p < 2.

Front

How do you check the solution of an inequality?

Back

Substitute a value from the solution set back into the original inequality to see if it holds true.

Front

What is the first step in solving the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40.

Front

What is the final solution for the inequality -4x + 14 ≤ 54?

Back

x ≥ -10.