Solving Two-Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. For example, in the inequality 2x + 3 < 7, you would first subtract 3 from both sides and then divide by 2.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

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

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves drawing a number line and indicating the range of values that satisfy the inequality, often using an open or closed circle to show whether endpoints are included.

Front

What is the solution to the inequality 7n - 1 > 76?

Back

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11.

Front

When do you flip the inequality sign?

Back

You flip the inequality sign when you multiply or divide both sides of the inequality by a negative number.

Front

Solve for k in the inequality 2k - 9 ≤ -19.

Back

Add 9 to both sides: 2k ≤ -10. Then divide by 2: k ≤ -5.

Front

What is the solution to the inequality r - 14 ≥ 17?

Back

Add 14 to both sides: r ≥ 31.

Front

What is the difference between ≤ and < in inequalities?

Back

The symbol ≤ means 'less than or equal to', while < means 'less than'. The former includes the endpoint, while the latter does not.

Front

How do you check if your solution to an inequality is correct?

Back

Substitute the solution back into the original inequality to see if it holds true.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution if there are no values that satisfy it, such as x + 2 < x.