Algebra - Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (>, <, ≥, ≤) to show that one expression is greater than, less than, or equal to another.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

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

Front

What is the solution set for the inequality x ≥ -10?

Back

The solution set includes all real numbers greater than or equal to -10.

Front

If you have a budget of $120 and each day of truck rental costs $39, how much is left for mileage after 2 days?

Back

After 2 days, the cost is 2 * $39 = $78. So, $120 - $78 = $42 is left for mileage.

Front

How do you express the cost of mileage if it is $0.25 per mile?

Back

The cost of mileage can be expressed as 0.25m, where m is the number of miles driven.

Front

If you have $42 left for mileage, how many miles can you drive?

Back

You can drive 42 / 0.25 = 168 miles.

Front

What is the solution to the inequality -3x ≤ 18?

Back

To solve, divide by -3 (flip the inequality sign): x ≥ -6.

Front

Which of the following is a solution to the inequality x ≤ 10? -2, -1, 0, 2

Back

All options (-2, -1, 0, 2) are solutions since they are all less than or equal to 10.