Inequalities (Part 2)

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

How do you solve the inequality -4a ≤ -28?

Back

Divide both sides by -4, remembering to reverse the inequality sign: a ≥ 7.

Front

What does the inequality a ≥ 11 represent graphically?

Back

It represents all values of 'a' that are greater than or equal to 11, including 11 itself.

Front

What is the solution to the inequality -4(5x + 3) - 6x > 11 - 3x?

Back

The solution is x < -1.

Front

How do you check if m = -2 is a solution for -8(m + 2) < 4(5 + 2m)?

Back

Substitute m = -2 into the inequality: -8(-2 + 2) < 4(5 + 2(-2)) simplifies to 0 < 0, which is false.

Front

What does the statement 'You must be at least 56" tall to ride this ride' translate to in inequality form?

Back

h ≥ 56.

Front

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

Back

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

Front

How do you graph the solution set of an inequality?

Back

You plot the boundary point and use an open circle for '>' or '<', and a closed circle for '≥' or '≤'.

Front

What is a boundary point in an inequality?

Back

A boundary point is the value that separates the solution set from the non-solution set.