Inequalities on a budget flashcards

What is an inequality?

An inequality shows a relationship where one value is not equal to another, using symbols like <, >, ≤, or ≥.

Solve: 2x + 3 < 11

x < 4. Subtract 3 from both sides, then divide by 2.

True or false: 5 < 3

False, because 5 is greater than 3.

Difference between ≤ and <

≤ includes the value (equal), while < does not (strictly less).

If x ≥ 10, what numbers satisfy this?

Any number 10 or greater, like 10, 12, or 100.

Graph: x < 2

A number line showing an open circle at 2, shading left.

True or false: x + 5 ≤ 10 leads to x ≤ 5

True, because subtracting 5 gives you x ≤ 5.

Solve: -3x > 9

x < -3. Divide both sides by -3 and flip the inequality.

What does 'at least' mean in inequalities?

'At least' means the value is greater than or equal to a number.

If 3x + 1 > 10, solve for x.

x > 3. Subtract 1, then divide by 3.

Fill in the blank: x ≤ 0 means...

...x can be zero or any negative number.

Example of a real-world inequality:

A store has at least 20 items in stock.

What does 'more than' indicate?

'More than' indicates a strict inequality, using >.

Graph solution: x ≥ 5

Closed circle at 5, shading to the right.

True or false: 7 is a solution to x < 10.

True, since 7 is less than 10.