Multistep Inequalities

Front

What is a multistep inequality?

Back

A multistep 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 -138 ≥ -6(6b − 7)?

Back

First, distribute -6: -138 ≥ -36b + 42. Then, subtract 42 from both sides: -180 ≥ -36b. Finally, divide by -36 (remember to flip the inequality): b ≥ 5.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Front

Solve the inequality 3 < -5n + 2n.

Back

Combine like terms: 3 < -3n. Divide by -3 (flip the sign): n < -1.

Front

What is the solution to the inequality 6x + 2 < 14?

Back

Subtract 2 from both sides: 6x < 12. Then divide by 6: x < 2.

Front

How do you isolate the variable in the inequality 28 − k ≥ 7(k − 4)?

Back

Distribute 7: 28 - k ≥ 7k - 28. Add k to both sides: 28 ≥ 8k - 28. Add 28: 56 ≥ 8k. Divide by 8: 7 ≥ k or k ≤ 7.

Front

What is the solution to the inequality -3 − 6(4x + 6) > -111?

Back

Distribute -6: -3 - 24x - 36 > -111. Combine like terms: -24x - 39 > -111. Add 39: -24x > -72. Divide by -24 (flip the sign): x < 3.

Front

What is the importance of checking your solution in inequalities?

Back

Checking your solution ensures that the values satisfy the original inequality, confirming that the solution is correct.

Front

What is a compound inequality?

Back

A compound inequality consists of two or more inequalities joined by 'and' or 'or', representing a range of values.

Front

How do you graph the solution of an inequality?

Back

To graph an inequality, use a number line, shading the region that represents the solution set and using open or closed circles to indicate whether endpoints are included.