Day 81 - Inequalities Practice for Benchmark

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 -5z - 7 ≤ 3?

Back

Add 7 to both sides to get -5z ≤ 10, then divide by -5 (remember to flip the inequality) to find z ≥ -2.

Front

What is the solution to the inequality -5(r - 1) < 6r - 17?

Back

Distributing gives -5r + 5 < 6r - 17. Adding 5r to both sides gives 5 < 11r - 17, then adding 17 gives 22 < 11r, so r > 2.

Front

What is the first step in solving the inequality 81 ≤ -7(3x + 3) + 4x?

Back

Distribute -7 to get 81 ≤ -21x - 21 + 4x.

Front

What is the solution to the inequality 18 ≥ 5k + 4k?

Back

Combine like terms to get 18 ≥ 9k, then divide by 9 to find k ≤ 2.

Front

What is the importance of flipping the inequality sign when multiplying or dividing by a negative number?

Back

Flipping the inequality sign ensures that the relationship between the two sides of the inequality remains true.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality, often resulting in a contradiction.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, often using 'and' or 'or' to connect them.