## Decide whether a number is a solution of a linear

Decide whether a number is a solution of a linear

equation. If the variable in an equation can be replaced by a real number

that makes the statement true, then that number is a solution of the equation.

For example, 8 is a solution of the equation x – 3 = 5, since replacing x

with 8 gives a true statement, 8 – 3 = 5. An equation is solved by finding

its solution set, the set of all solutions. The solution set of the equation

x – 3 = 5 is {8}.

Equivalent equations are equations that have the same solution set. To

solve an equation, we usually start with the given equation and replace it

with a series of simpler equivalent equations. For example,

5x + 2 =17, 5x = 15, and x = 3  Equivalent equations

are all equivalent since each has the solution set {3}.

## Find the reciprocal of a number

Find the reciprocal of a number

Earlier, subtraction was defined in terms of addition. Now, division is defined in terms of multiplication. The definition of division depends on the idea of a multiplicative

inverse or reciprocal; two numbers are reciprocals if they have a product of 1.

Reciprocal

The reciprocal of a nonzero number a is  .

## Use number lines

Use number lines

A good way to get a picture of a set

of numbers is by using a number line. To construct a number line, choose

any point on a horizontal line and label it 0. Next, choose a point to the right

of 0 and label it 1. The distance from 0 to 1 establishes a scale that can be

used to locate more points, with positive numbers to the right of 0 and negative

numbers to the left of 0. The number 0 is neither positive nor negative.

A number line is shown in Figure 1.

The set of numbers identified on the number line in Figure 1, including

positive and negative numbers and 0, is part of the set of integers, written

I 5 {. . . , 23, 22, 21, 0, 1, 2, 3, . . . }.

Each number on a number line is called the coordinate of the point that

it labels, while the point is the graph of the number. Figure 2 shows a number

line with several selected points graphed on it.