Solving inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≤' mean?

Back

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

Front

What does the symbol '≥' mean?

Back

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

Front

How do you solve the inequality s - 10 ≤ 1?

Back

Add 10 to both sides: s ≤ 11.

Front

What is the solution to the inequality 2(b - 8) > 12?

Back

First, divide both sides by 2: b - 8 > 6. Then add 8: b > 14.

Front

How do you solve the inequality 10 ≥ x - 3?

Back

Add 3 to both sides: 10 + 3 ≥ x, which simplifies to x ≤ 13.

Front

When do you flip the inequality symbol?

Back

You flip the inequality symbol when you multiply or divide both sides by a negative number.

Front

How do you solve the inequality -4d - 9 ≤ 3?

Back

Add 9 to both sides: -4d ≤ 12. Then divide by -4 (flip the symbol): d ≥ -3.

Front

What is the solution set for the inequality x + 5 < 12?

Back

Subtract 5 from both sides: x < 7.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality means to represent the solution set on a number line, using an open circle for < or > and a closed circle for ≤ or ≥.