Solving Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that a value can be either less than or equal to another value.

Front

Translate: 'At most 45' into an inequality.

Back

g ≤ 45.

Front

What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. It indicates that one value is larger than another.

Front

How do you solve the inequality 6x + 10 > 5x - 12?

Back

Subtract 5x from both sides: x + 10 > -12. Then, subtract 10: x > -22.

Front

What is the solution to the inequality 77 ≤ 5 + 8n?

Back

n ≥ 9.

Front

How do you graph the inequality x < 4?

Back

Draw a number line, place an open circle at 4, and shade to the left.

Front

What does the solution x < -4 represent on a number line?

Back

It represents all numbers less than -4, shown with an open circle at -4 and shading to the left.

Front

What is the first step in solving the inequality 3(x - 2) < 2(x + 9)?

Back

Distribute: 3x - 6 < 2x + 18.

Front

What is the solution to the inequality 3(x - 2) < 2(x + 9)?

Back

x < 24.