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# Algebra: GED Test Prep (page 5)

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### Inequalities

Linear inequalities are solved in much the same way as simple equations. The most important difference is that when an inequality is multiplied or divided by a negative number, the inequality symbol changes direction.

Example

10 > 5, but if you multiply by –3, (10)(–3) < (5)(–3) –30 < –15

### Solving Linear Inequalities

To solve a linear inequality, isolate the letter and solve the same as you would in an equation. Remember to reverse the direction of the inequality sign if you divide or multiply both sides of the equation by a negative number.

Example

If 7 – 2x > 21, find x.

Isolate the variable.

7 – 2x > 21

7 – 2x – 7 > 21 – 7

–2x > 14

Because you are dividing by a negative number, the direction of the inequality symbol changes direction.

x < –7

The answer consists of all real numbers less than –7.

### Exponents

An exponent tells you how many times the number, called the base, is a factor in the product.

Example

Sometimes you will see an exponent with a variable:

bn

The b represents a number that will be a factor to itself n times.

Example

bn where b = 5 and n = 3

Don't let the variables fool you. Most expressions are very easy once you substitute in numbers.

bn = 53 = 5 × 5 × 5 = 125

### Laws of Exponents

• Any base to the zero power is always 1.
• 50 = 1   700 = 1   29,8740 = 1

• When you multiply identical bases, add the exponents.
• 22 × 24 × 26 = 212   a2 × a3 × a5 = a10

• When you divide identical bases, subtract the exponents.
• Here is another method of illustrating multiplication and division of exponents:
• bm × bn = bm + n

bmbn = bmn

• If an exponent appears outside of parentheses, you multiply the exponents together.
• (33)7 = 321

(g4)3 = g12

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