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 - 2 ≤ -22?

Back

Add 2 to both sides: 4x ≤ -20. Then divide by 4: x ≤ -5.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality means representing the solution set on a number line, using an open or closed circle to indicate whether the endpoint is included.

Front

If n/3 - 7 ≤ -3, how do you solve for n?

Back

Multiply both sides by 3: n - 21 ≤ -9. Then add 21: n ≤ 12.

Front

In the context of inequalities, what does 'at least' mean?

Back

'At least' means the value is greater than or equal to a certain number.

Front

If Lea needs at least $240 and has saved $30, how do you express the amount she needs to earn?

Back

Let x be the number of cars washed. The inequality is 30 + 14x ≥ 240.

Front

What is the first step to solve the inequality 7n - 1 > 76?

Back

Add 1 to both sides: 7n > 77.