Multi-Step Inequalities

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality: 14 < -2a + 6 - 2a?

Back

Combine like terms to get 14 < -4a + 6, then isolate a to find a < -2.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or exactly equal to the number.

Front

How do you graph the solution set of the inequality -4a ≤ -28?

Back

Divide both sides by -4 (remember to flip the inequality sign) to get a ≥ 7, then graph a solid dot at 7 and shade to the right.

Front

What is the first step to solve the inequality 6x + 2 + 6x < 14?

Back

Combine like terms to simplify it to 12x + 2 < 14.

Front

What is the solution to the inequality 4(2a + 3) < 3(a - 1)?

Back

Distribute to get 8a + 12 < 3a - 3, then isolate a to find a < -3.

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 opposite side.

Front

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

Back

Subtract 14 from both sides to get -4x ≤ 40, then divide by -4 (flipping the inequality) to find x ≥ -10.

Front

How do you interpret the solution x < 1 on a number line?

Back

It means that all numbers to the left of 1, not including 1 itself, are solutions to the inequality.

Front

What is the importance of flipping the inequality sign when multiplying or dividing by a negative number?

Back

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