Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality 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 10.25h ≥ 550?

Back

To solve for h, divide both sides by 10.25: h ≥ 550 / 10.25, which simplifies to h ≥ 53.66, rounding up gives h ≥ 54.

Front

When do you flip the inequality symbol?

Back

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

Front

What is the solution to the inequality 4x + 1 > 13?

Back

To solve, subtract 1 from both sides: 4x > 12, then divide by 4: x > 3.

Front

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

Back

To solve, subtract 14 from both sides: -4x ≤ 40, then divide by -4 (flipping the inequality): x ≥ -10.

Front

What does an open dot represent when graphing an inequality?

Back

An open dot represents that the number is not included in the solution set, used for < or >.

Front

What does a closed dot represent when graphing an inequality?

Back

A closed dot represents that the number is included in the solution set, used for ≤ or ≥.

Front

How do you graph the inequality x < 3?

Back

Draw a number line, place an open dot at 3, and shade to the left.