Solving Multistep Inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable in an inequality, perform inverse operations on both sides of the inequality, similar to solving an equation, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What does it mean to reverse the inequality sign?

Back

Reversing the inequality sign means changing 'greater than' to 'less than' or vice versa, which occurs when you multiply or divide both sides of an inequality by a negative number.

Front

Solve: 7(x + 3) < 5x + 13

Back

x < -4

Front

Solve: -3 − 6(4x + 6) > -111

Back

x < 3

Front

Solve: 3 < -5n + 2n

Back

n < -1

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality, often represented on a number line.

Front

Solve the inequality: 4(5x + 2) ≤ 28

Back

x ≤ 1

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

What does it mean when an inequality has no solution?

Back

An inequality has no solution when there are no values that can satisfy the inequality, often resulting in a contradiction.