Writing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is less than, greater 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 y + 7 ≥ 12?

Back

Subtract 7 from both sides: y ≥ 12 - 7, which simplifies to y ≥ 5.

Front

How do you solve the inequality w + 4 ≤ -5?

Back

Subtract 4 from both sides: w ≤ -5 - 4, which simplifies to w ≤ -9.

Front

What does the inequality x + 4 ≤ 19 represent in a real-world context?

Back

It represents that the current height of a tree (4 feet) plus its growth (x feet) must be less than or equal to its maximum height (19 feet).

Front

How do you set up an inequality for a total cost less than $1,000 with a service fee of $175?

Back

The inequality is x + 175 < 1000, where x represents the food fee.

Front

How do you represent Johnny's earnings in an inequality if he wants to earn at least $105?

Back

The inequality is 15h ≥ 105, where h is the number of hours he works.

Front

What is the first step in solving the inequality 15h ≥ 105?

Back

Divide both sides by 15: h ≥ 105 / 15, which simplifies to h ≥ 7.

Front

What is the solution set for the inequality y + 7 < 12?

Back

Subtract 7 from both sides: y < 12 - 7, which simplifies to y < 5.