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 -3x - 4 < 5?

Back

Add 4 to both sides: -3x < 9. Then divide by -3 (remember to flip the inequality): x > -3.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value can be either greater than or equal to a certain number.

Front

Solve the inequality: 2x + 6 ≥ -8.

Back

Subtract 6 from both sides: 2x ≥ -14. Then divide by 2: x ≥ -7.

Front

What is the first step in solving the inequality 2k - 9 ≤ -19?

Back

Add 9 to both sides: 2k ≤ -10.

Front

How do you graph the solution of an inequality?

Back

To graph an inequality, draw a number line, use an open circle for < or > (not including the number) and a closed circle for ≤ or ≥ (including the number). Shade the region that satisfies the inequality.

Front

What does the solution k ≤ -5 represent?

Back

It means that k can be any number less than or equal to -5.

Front

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 m < 3?

Back

It means that m can be any number less than 3.

Front

What is the importance of flipping the inequality sign when multiplying or dividing by a negative number?

Back

Flipping the inequality sign ensures that the relationship between the numbers remains true. For example, if -2x > 4, dividing by -2 flips the sign to x < -2.