Solve 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 often involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 11 > -3y + 2?

Back

First, subtract 2 from both sides: 11 - 2 > -3y. Then, simplify: 9 > -3y. Finally, divide by -3 (remember to flip the inequality): -3 < y.

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, and is represented by a closed dot at -7 and a line extending to the right.

Front

How do you graph the inequality 3 + 9k > 111?

Back

First, solve for k: 9k > 108, then k > 12. Graph it with an open dot at 12 and a line extending to the right.

Front

What is the first step to solve the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40.

Front

What does the inequality u/7 – 1 ≤ 1 represent?

Back

It represents that the value of u divided by 7, minus 1, is less than or equal to 1.

Front

How do you isolate the variable in the inequality 2x + 6 ≥ -8?

Back

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

Front

What is the solution to the inequality -4x + 14 ≤ 54?

Back

x ≥ -10.

Front

What does the symbol '≥' mean in inequalities?

Back

It means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to the number.

Front

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

Back

u ≤ 14.