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 -4a + 6 > 14, then isolate a to find a < -2.

Front

What does the solution a < -2 represent on a number line?

Back

It represents all numbers to the left of -2, not including -2 itself.

Front

What is the first step in solving the inequality -4a ≤ -28?

Back

Divide both sides by -4, remembering to reverse the inequality sign, resulting in a ≥ 7.

Front

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

Back

Plot a closed circle at 7 and shade to the right to indicate all values greater than or equal to 7.

Front

What is the solution to the inequality -4(x + 3) ≥ 3(x - 4)?

Back

Distributing gives -4x - 12 ≥ 3x - 12. Combine like terms to find x ≤ 0.

Front

What does the solution x ≤ 0 indicate?

Back

It indicates that x can be any number less than or equal to 0.

Front

How do you solve the inequality -3 - 6(4x + 6) > -111?

Back

First, distribute -6 to get -3 - 24x - 36 > -111, then combine like terms and isolate x to find x < 3.

Front

What is the significance of reversing the inequality sign?

Back

The inequality sign is reversed when multiplying or dividing both sides of an inequality by a negative number.

Front

What is a solution set in the context of inequalities?

Back

A solution set is the set of all values that satisfy the inequality.