2-step Inequalities

Front

What is a 2-step inequality?

Back

A 2-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 7k - 2 ≥ -9?

Back

To solve 7k - 2 ≥ -9, first add 2 to both sides to get 7k ≥ -7, then divide both sides by 7 to find k ≥ -1.

Front

What is the first step in solving the inequality 6t + 4 ≤ -2?

Back

The first step is to subtract 4 from both sides, resulting in 6t ≤ -6.

Front

What does the inequality 2 + 3n ≤ 14 represent in a real-world context?

Back

It represents a situation where Juan's total spending on soda and nachos does not exceed $14, with the cost of soda being $2 and nachos costing $3 each.

Front

How do you isolate the variable in the inequality 3x - 2 ≥ 34?

Back

To isolate x, first add 2 to both sides to get 3x ≥ 36, then divide both sides by 3 to find x ≥ 12.

Front

What is the solution to the inequality 3x + 4 > 13?

Back

To solve 3x + 4 > 13, subtract 4 from both sides to get 3x > 9, then divide by 3 to find x > 3.

Front

What is the significance of the inequality symbol in 6t + 4 ≤ -2?

Back

The inequality symbol indicates that the value of the expression on the left is less than or equal to the value on the right, allowing for a range of possible solutions.

Front

What is the general approach to solving a 2-step inequality?

Back

The general approach involves performing inverse operations to isolate the variable, maintaining the direction of the inequality unless multiplying or dividing by a negative number.

Front

What happens to the inequality sign when multiplying or dividing by a negative number?

Back

When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

Front

How can you check your solution to an inequality?

Back

You can check your solution by substituting the value back into the original inequality to see if it holds true.