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 and then divide by 2.

Front

How do you solve the inequality y + 7 ≥ 12?

Back

Subtract 7 from both sides: y ≥ 12 - 7, which simplifies to y ≥ 5.

Front

What does the inequality 11 ≤ a mean?

Back

It means that 'a' can be 11 or any number greater than 11.

Front

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

Back

Subtract 14 from both sides: -4x ≤ 54 - 14, which simplifies to -4x ≤ 40. Then divide by -4 (remember to flip the inequality sign): x ≥ -10.

Front

What is the rule for flipping 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: 2k - 9 ≤ -19.

Back

Add 9 to both sides: 2k ≤ -19 + 9, which simplifies to 2k ≤ -10. Then divide by 2: k ≤ -5.

Front

What is the solution to the inequality -3x ≥ 12?

Back

Divide both sides by -3 (flip the sign): x ≤ -4.

Front

What does the symbol '≥' represent?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' represent?

Back

The symbol '≤' means 'less than or equal to'.

Front

If x + 5 < 10, what is the solution for x?

Back

Subtract 5 from both sides: x < 10 - 5, which simplifies to x < 5.