ANSWERS
- 120 miles
- 25o
- 216 cubic inches
- 20 feet
- 4 amperes
Solving Simple Equations
Anequationis a statement of equality of two algebraic expressions: e.g., 3þ 2
¼5 is an equation. An equation can contain one or more variables: e.g., xþ 7
¼10 is an equation with one variable, x. If an equation has no variables, it is
called aclosedequation. Closed equations can be either true or false: e.g., 6þ
8 ¼14 is a closed true equation, whereas 3þ 5 ¼6 is a false closed equation.
Open equations, also calledconditionalequations, are neither true nor false.
However, if a value for the variable is substituted in the equation and a closed
true equation results, the value is called asolutionorrootof the equation. For
example, when 3 is substituted for x in the equation xþ 7 ¼10, the resulting
equation 3þ 7 ¼10 is true, so 3 is called a solution of the equation. Finding
the solution of an equation is calledsolvingthe equation. The expression to
the left of the equal sign in an equation is called theleft memberorleft sideof
the equation. The expression to the right of the equal sign is called theright
memberorright sideof the equation.
In order to solve an equation, it is necessary to transform the equation into
a simpler equivalent equation with only the variable on one side and a con-
stant on the other side. There are four basic types of equations and four
principles that are used to solve them. These principles do not change the
nature of an equation: i.e., the simpler equivalent equation has the same
solution as the original equation.
In order tocheckan equation, substitute the value of the solution or root
for the variable in the original equation and see if a closed true equation
results.
An equation such as x 8 ¼ 22 can be solved by using theaddition
principle.The same number can be added to both sides of an equation without
changing the nature of the equation.
EXAMPLE
Solve x 8 ¼22.
CHAPTER 7 Expression and Equations 135