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. It often involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality -2x + 7 < 19?

Back

Subtract 7 from both sides: -2x < 12. Then divide by -2 (remember to flip the inequality): x > -6.

Front

What does the solution k ≥ -1 represent in a number line?

Back

It represents all numbers greater than or equal to -1, including -1 itself.

Front

How do you graph the solution of the inequality 3x + 2 > 14?

Back

First, solve for x: 3x > 12, so x > 4. On a number line, draw an open circle at 4 and shade to the right.

Front

What is the first step to solve the inequality 7k - 2 ≥ -9?

Back

Add 2 to both sides: 7k ≥ -7.

Front

What is the final solution for the inequality 6t + 4 ≤ -2?

Back

Subtract 4 from both sides: 6t ≤ -6, then divide by 6: t ≤ -1.

Front

What does the symbol '>' mean in inequalities?

Back

It 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

It means 'less than' and indicates that the value on the left is smaller than the value on the right.

Front

How do you solve the inequality 7n - 1 > 76?

Back

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

Front

What is the solution to the inequality 3x + 2 > 14?

Back

Subtract 2 from both sides: 3x > 12, then divide by 3: x > 4.