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 7k – 2 ≥ -9?

Back

Add 2 to both sides to get 7k ≥ -7, then divide by 7 to find k ≥ -1.

Front

What happens to the inequality sign when you divide by a negative number?

Back

You must flip the inequality sign when dividing or multiplying both sides of an inequality by a negative number.

Front

Solve for t: 6t + 4 ≤ -2.

Back

Subtract 4 from both sides to get 6t ≤ -6, then divide by 6 to find t ≤ -1.

Front

What is the solution to the equation 6n + 4 = -26?

Back

Subtract 4 from both sides to get 6n = -30, then divide by 6 to find n = -5.

Front

What does it mean to isolate a variable in an inequality?

Back

Isolating a variable means to manipulate the inequality so that the variable is on one side and all other terms are on the other side.

Front

What is the first step in solving the inequality -3x ≥ 12?

Back

Divide both sides by -3, remembering to flip the inequality sign, resulting in x ≤ -4.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

How do you check the solution of an inequality?

Back

Substitute the solution back into the original inequality to see if it makes the inequality true.

Front

What does the solution k ≥ -1 represent on a number line?

Back

It represents all numbers to the right of -1, including -1 itself.