solving inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you solve the inequality 7x + 15 ≥ -20?

Back

Subtract 15 from both sides: 7x ≥ -35. Then divide by 7: x ≥ -5.

Front

What is the solution to the inequality 9x + 3 < 21?

Back

Subtract 3 from both sides: 9x < 18. Then divide by 9: x < 2.

Front

How do you solve the inequality 10 < 3x + 19?

Back

Subtract 19 from both sides: -9 < 3x. Then divide by 3: x > -3.

Front

What is the solution to the inequality 4x + 14 ≤ 54?

Back

Subtract 14 from both sides: 4x ≤ 40. Then divide by 4: x ≤ 10.

Front

When graphing an inequality, what does a closed dot indicate?

Back

A closed dot indicates that the number is included in the solution (used for ≤ and ≥).

Front

What does an open dot indicate when graphing an inequality?

Back

An open dot indicates that the number is not included in the solution (used for < and >).

Front

What is the first step in solving inequalities?

Back

The first step is to isolate the variable on one side of the inequality.