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, 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 -5t + 9 = 24?

Back

The first step is to isolate the term with the variable by subtracting 9 from both sides, resulting in -5t = 15.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

First, subtract 14 from both sides to get -4x ≤ 40, then divide by -4 (remember to flip the inequality sign) to find x ≥ -10.

Front

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

Back

Flipping the inequality sign means that if you divide or multiply both sides of an inequality by a negative number, the direction of the inequality changes.

Front

How do you solve the inequality 2x + 6 ≥ -8?

Back

Subtract 6 from both sides to get 2x ≥ -14, then divide by 2 to find x ≥ -7.

Front

What is the solution to the inequality u/7 - 1 ≤ 1?

Back

To solve u/7 - 1 ≤ 1, first add 1 to both sides to get u/7 ≤ 2, then multiply both sides by 7 to find u ≤ 14.

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.

Front

What are the steps to graph a solution to a two-step inequality?

Back

1. Solve the inequality for the variable. 2. Plot the boundary point on a number line. 3. Use an open circle for < or > and a closed circle for ≤ or ≥. 4. Shade the appropriate region.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary point, while a non-strict inequality (≤ or ≥) includes the boundary point.