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14 Solving Linear Equations and Inequalities
A linear equation in one variable, say x, has the standard form ax + b = c,
a ≠ 0, where a, b, and c are constants. For example, 3x − 7 = 14 is a linear
equation in standard form. An equation has two sides. The expression on the
left side of the equal sign is the left side of the equation, and the expression
on the right side of the equal sign is the right side of the equation.Solving One-Variable Linear Equations
To solve a linear equation that has one variable x means to fi nd a numerical
value for x that makes the equation true. An equation is true when the left
side has the same value as the right side. When you solve an equation, you
undo what has been done to x until you get an expression like this: x = a num-
ber. As you proceed, you exploit the fact that addition and subtraction undo
each other; and, similarly, multiplication and division undo one another.The goal in solving a linear equation is to get the variable by itself on only
one side of the equation and with a coeffi cient of 1 (usually understood).You solve an equation using the properties of real numbers and simple
algebraic tools. An equation is like a balance scale. To keep the equation in
balance, when you do something to one side of the equation, you must do to
the same thing to the other side of the equation.P