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 '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 -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What is the solution to the inequality 4x + 5 ≥ 41?

Back

Subtract 5 from both sides: 4x ≥ 36. Then divide by 4: x ≥ 9.

Front

What does a closed dot on a number line indicate?

Back

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

Front

What does an open dot on a number line indicate?

Back

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

Front

How do you graph the inequality x ≥ 3?

Back

Draw a number line, place a closed dot on 3, and shade to the right.

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

What is the difference between '>' and '≥'?

Back

'>' means greater than (not including the number), while '≥' means greater than or equal to (including the number).