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# Algebra Review Help (page 4)

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#### Example 1:

A number increased by five = x + 5.

A number decreased by five = x – 5.

• "Less than" means subtract.

#### Example 2:

Ten less than a number = x – 10.

Ten more than a number = x + 10.

• "Times" or "product" means multiply.
• "Divisible" or "quotient" means divide.

#### Example 3:

Three times a number = 3x.

Three is divisible by a number = 3 ÷ x.

• "Times the sum" means to multiply a number by a quantity.

#### Example 4:

Five times the sum of a number and three = 5(x + 3).

• Two variables are sometimes used together.

#### Example 5:

A number y exceeds five times a number x by ten.

y = 5x + 10

• Inequality signs are used for "at least" and "at most," as well as "less than" and "more than."

#### Example 6:

The product of x and 6 is greater than 2.

x · 6 > 2

When 14 is added to a number x, the sum is less than 21.

x + 14 < 21

The sum of a number x and four is at least nine.

x + 4 ≥ 9

When seven is subtracted from a number x, the difference is at most four.

## Absolute Value Inequalities

|x| < a is equivalent to –a < x < a, and |x| > a is equivalent to x > a or x < –a.

#### Example

|x + 3| > 7

x + 3 >7 or x + 3 < –7

x > 4       x < –10

Thus, x > 4 or x < –10.

Find practice problems and solutions for these concepts at Algebra Review Practice Problems.

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