ELL 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 operations such as addition, subtraction, multiplication, or division.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable in an inequality, perform inverse operations (addition, subtraction, multiplication, division) on both sides of the inequality, ensuring to reverse the inequality sign when multiplying or dividing by a negative number.

Front

Solve the inequality: 3(k-5) + 9k ≥ -3

Back

k ≥ 1

Front

Solve the inequality: 3(x - 2) < 2(x + 9)

Back

x < 24

Front

Back

Front

Solve the inequality: 10 < 3x + 19

Back

x > -3

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

How do you graph the solution of an inequality on a number line?

Back

To graph the solution of an inequality on a number line, use an open circle for < or > (not including the endpoint) and a closed circle for ≤ or ≥ (including the endpoint). Shade the region that represents the solution.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the endpoint, while non-strict inequalities (≤, ≥) do include the endpoint.