Solving 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 28 - k ≥ 7(k - 4)?

Back

First, distribute the 7: 28 - k ≥ 7k - 28. Then, add k to both sides: 28 ≥ 8k - 28. Next, add 28 to both sides: 56 ≥ 8k. Finally, divide by 8: k ≤ 7.

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 3 < -5n + 2n?

Back

Combine like terms: 3 < -3n. Then, divide by -3 (remember to flip the inequality): n < -1.

Front

What does it mean to flip the inequality sign when dividing by a negative number?

Back

When you divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

Front

What is the first step in solving the inequality 7(x + 3) < 5x + 13?

Back

Distribute the 7: 7x + 21 < 5x + 13.

Front

How do you combine like terms in the inequality 7x + 21 < 5x + 13?

Back

Subtract 5x from both sides: 2x + 21 < 13.

Front

What is the next step after simplifying 2x + 21 < 13?

Back

Subtract 21 from both sides: 2x < -8.

Front

How do you solve for x in the inequality 2x < -8?

Back

Divide both sides by 2: x < -4.

Front

What is the importance of checking your solution in an inequality?

Back

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