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 -7x + 15 ≥ -20?

Back

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

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 9x + 3 < 21?

Back

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

Front

How do you solve the inequality 4x + 5 ≥ 41?

Back

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

Front

What is the difference between 'strict' and 'non-strict' inequalities?

Back

Strict inequalities use < or >, while non-strict inequalities use ≤ or ≥.

Front

What does it mean to graph an inequality on a number line?

Back

Graphing an inequality involves shading the region of the number line that satisfies the inequality and using an open or closed dot to indicate whether the endpoint is included.