Solving Multistep Inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, or division.

Front

How do you represent a real-world situation with an inequality?

Back

Identify the variables, constants, and relationships in the situation, then translate them into an inequality using appropriate symbols (>, <, ≥, ≤).

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left can be greater than or equal to the value on the right.

Front

How do you solve the inequality 2x + 3 < 11?

Back

Subtract 3 from both sides to get 2x < 8, then divide by 2 to find x < 4.

Front

What is the first step in solving the inequality 3x - 5 ≥ 10?

Back

Add 5 to both sides to isolate the term with x, resulting in 3x ≥ 15.

Front

How do you check the solution of an inequality?

Back

Substitute the solution back into the original inequality to see if it holds true.

Front

What is the solution set of the inequality x + 4 < 10?

Back

The solution set is x < 6.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality, often resulting from contradictory statements.

Front

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

Back

Use an open circle for < or > and a closed circle for ≤ or ≥, then shade the region that represents the solution set.