Solving inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or equal to the other.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you solve the inequality -3 + x ≤ -11?

Back

Add 3 to both sides: x ≤ -8.

Front

Translate: A number increased by 4 is no more than -18.

Back

x + 4 ≤ -18.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you represent the scenario: Penelope can spend no more than $35 at the carnival?

Back

0.50x + 20 ≤ 35, where x is the number of ride tickets.

Front

Translate: 5 times a number is at least 60.

Back

5x ≥ 60.

Front

How do you solve the inequality 2x - 3 ≥ 4x - 1?

Back

Rearranging gives: -3 + 1 ≥ 4x - 2x, which simplifies to x ≤ -1.

Front

What is the first step in solving an inequality?

Back

Isolate the variable on one side of the inequality.

Front

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

Back

'>' means greater than, while '≥' means greater than or equal to.