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

First, combine like terms: -4a + 6. Then, isolate a: 14 - 6 < -4a leads to 8 < -4a, which simplifies to a < -2.

Front

What does the inequality a > 6 represent on a number line?

Back

It represents all numbers greater than 6, which is shown as an open circle at 6 and a line extending to the right.

Front

What is the solution to the inequality 6x + 2 + 6x < 14?

Back

Combine like terms to get 12x + 2 < 14. Subtract 2 from both sides to get 12x < 12, then divide by 12 to find x < 1.

Front

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

Back

First, solve for a: a ≥ 7. Then, graph a closed circle at 7 and shade to the right.

Front

What does the inequality k ≥ -7 mean?

Back

It means k can be any number greater than or equal to -7.

Front

What is the first step in solving the inequality 28 - k ≥ 7(k - 4)?

Back

Distribute the 7 on the right side: 28 - k ≥ 7k - 28.

Front

What is the solution to the inequality a > -24?

Back

The solution is all numbers greater than -24, represented by an open circle at -24 and shading to the right.

Front

What does the inequality a < -2 indicate about the value of a?

Back

It indicates that a can be any number less than -2.

Front

How do you isolate the variable in the inequality 6x + 2 < 14?

Back

Subtract 2 from both sides to get 6x < 12, then divide by 6 to find x < 2.