Math: Translating Inequalities

Vocabulary:

Inequality: A mathematical sentence that compares the values of two expressions using an inequality symbol.-Solution of an inequality: Any value or values of a variable in the inequality that makses an inequality true.

Solution of an inequality: Any value or values of a variable in the inequality that makes an inequality true.

For example, if I had x > 3, I know that any number that is bigger than 3 will make my inequality true. 3.1, 4, 100, and 200 are all possible solutions of an inequality because if I plug them in for x, my inequality will be true.

Lesson:

There are four inequality symbols:

< = less than
> = greater than
≥ = greater than or equal to
≤ = less than or equal to

When we are translating inequalities, we think back to what we know already about translating verbal expressions into algebraic expressions.

We have to pay attention to key words. Here are some to remind you:

Increase = +(plus)
Decrease = - (minus)
Is = = (equals)
Sum +
Difference -
Product x
Quotient (divide)
More than +
Less than -
Twice (multiply by two)

When we are solving inequalties, there are key words that help us know what to do and what sign to use when we see them:

< = less than
> = greater than, more than
≥ = greater than or equal to, more than or equal to, no less than, at least
≤ = less than or equal to, no more than, at most

Let's try it:

Two times a number is less than eight.

We know that two times a number = 2x

Then, we are told that 2x is less than eight.

We plug in the less than sign, <, and then we have 2x <

Now, we have to put in the eight and then we are left with: 2x < 8.