Solving Multi Step Inequalities

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality 6x + 10 > 5x - 12?

Back

Subtract 5x from both sides: x + 10 > -12. Then, subtract 10 from both sides: x > -22.

Front

What does the inequality m > 41 represent in a real-world context?

Back

It means that the quantity m is greater than 41, such as Mary’s points totaling more than 41.

Front

How do you solve the inequality 10 < 3x + 19?

Back

Subtract 19 from both sides: -9 < 3x. Then, divide by 3: -3 < x or x > -3.

Front

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

Back

Subtract 14 from both sides: -4x ≤ 40. Then, divide by -4 (remember to flip the inequality): x ≥ -10.

Front

How do you solve the inequality 6(n + 2) < -72?

Back

Distribute: 6n + 12 < -72. Subtract 12: 6n < -84. Divide by 6: n < -14.

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than' and indicates that the value on the left is larger than the value on the right.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to' and indicates that the value on the left is either less than or equal to the value on the right.

Front

What is the first step in solving a multi-step inequality?

Back

The first step is to simplify both sides of the inequality, which may involve combining like terms or distributing.

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 flip the inequality sign.