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, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≥' represent in inequalities?

Back

'≥' means 'greater than or equal to'.

Front

How do you solve the inequality -9x + 7 ≥ 25?

Back

Subtract 7 from both sides to get -9x ≥ 18, then divide by -9 (remember to flip the inequality sign) to find x ≤ -2.

Front

What is the first step in solving the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides to isolate the term with x.

Front

How do you interpret the solution x ≥ -10?

Back

This means that x can be any number greater than or equal to -10.

Front

What is the process to solve the inequality 6 + 2h > 30?

Back

Subtract 6 from both sides to get 2h > 24, then divide by 2 to find h > 12.

Front

How do you write an inequality for Sam's earnings to buy a laptop?

Back

Let h be the number of hours worked. The inequality is 10.25h ≥ 550.

Front

What does it mean to round to the next higher hour in the context of working hours?

Back

If the calculated hours are not a whole number, round up to the nearest whole number.

Front

What is the solution to the inequality 10.25h ≥ 550?

Back

h must be at least 54 hours.

Front

What does the solution 'h > 12' indicate about the value of h?

Back

h must be any number greater than 12.