2.4 Solving 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, adding or subtracting, and multiplying or dividing by negative numbers.

Front

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

Back

First, combine like terms: -2a - 2a = -4a. Then, rearrange: 14 - 6 > -4a, which simplifies to 8 > -4a. Dividing by -4 (and flipping the inequality) gives a < -2.

Front

What does the inequality 9 ≥ -2m + 2 - 3 represent?

Back

This inequality can be solved by simplifying the right side: 9 ≥ -2m - 1. Rearranging gives 10 ≥ -2m, which simplifies to m ≥ -5 after dividing by -2.

Front

What is the solution to the inequality -p - 4p > -10?

Back

Combine like terms: -5p > -10. Dividing by -5 (and flipping the inequality) gives p < 2.

Front

Which graph represents the inequality -2 ≥ n?

Back

Graph A represents the inequality -2 ≥ n, indicating that n can take values less than or equal to -2.

Front

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

Back

First, subtract 14 from both sides: -4x ≤ 40. Then, divide by -4 (flipping the inequality) to get x ≥ -10.

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.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution when the two sides cannot be made equal or when the conditions contradict each other, such as x < 2 and x > 3.

Front

What is the graphical representation of an inequality?

Back

The graphical representation of an inequality shows a number line with a shaded region indicating all possible solutions, often with an open or closed circle to denote whether endpoints are included.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (e.g., < or >) does not include the endpoint, while a non-strict inequality (e.g., ≤ or ≥) includes the endpoint.