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 (>, <, ≥, ≤).

Front

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

Back

The symbol '>' means 'greater than'. It indicates that the value on the left is larger than the value on the right.

Front

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

Back

The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either larger than or equal to the value on the right.

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either smaller than or equal to the value on the right.

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

How do you solve the inequality -7 + 10z > -27?

Back

Add 7 to both sides: 10z > -20. Then divide by 10: z > -2.

Front

What does the number line graph representing x < -4 look like?

Back

It shows an open circle at -4 and a line extending to the left, indicating all values less than -4.

Front

How do you solve the inequality 5z - 2 - 2z < 13?

Back

Combine like terms: 3z - 2 < 13. Add 2: 3z < 15. Then divide by 3: z < 5.

Front

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

Back

Subtract 5 from both sides: 72 ≤ 8n. Then divide by 8: 9 ≤ n or n ≥ 9.