7.9 HW 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. It typically involves addition or subtraction followed by multiplication or division.

Front

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

Back

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 5b - 6 = 24?

Back

Add 6 to both sides to isolate the term with the variable.

Front

What does the solution x ≥ -7 mean in terms of a number line?

Back

It means that x can be any number greater than or equal to -7, including -7 itself.

Front

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

Back

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

Front

What is the solution to the inequality 2k - 9 ≤ -19?

Back

Add 9 to both sides to get 2k ≤ -10, then divide by 2 to find k ≤ -5.

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What is the process to 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 importance of flipping the inequality sign when dividing by a negative number?

Back

Flipping the inequality sign ensures that the relationship between the two sides of the inequality remains true.

Front

How do you check the solution of an inequality?

Back

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