Solving & Graphing 1-Variable 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

'≥' means 'greater than or equal to'.

Front

How do you solve the inequality 4x − 7 ≥ 21?

Back

Add 7 to both sides: 4x ≥ 28. Then divide by 4: x ≥ 7.

Front

What is the solution set of the inequality –4n + 1 > –23?

Back

First, subtract 1 from both sides: -4n > -24. Then divide by -4 (remember to flip the inequality): n < 6.

Front

How do you express 'Twice a number x, plus 8 is greater than 12' as an inequality?

Back

2x + 8 > 12.

Front

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

Back

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

Front

What does the number line graph representing x ≥ 3 look like?

Back

A solid dot at 3 and a line extending to the right.

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).

Front

How do you graph the solution set of an inequality?

Back

Identify the boundary point, use an open dot for '>' or '<', and a closed dot for '≥' or '≤'. Shade the appropriate side.

Front

What is the first step in solving the inequality 2x + 5 < 15?

Back

Subtract 5 from both sides: 2x < 10.