Idiot\'s Guides Basic Math and Pre-Algebra

124 Part 2: Into the Unknown

There are four operations of arithmetic so here’s the fourth example. In this one, you see division,

so use multiplication to solve it.

Solve the equation x

7

 31.

The variable was divided by 7 and the answer was 31. To find the value of the variable, multiply

both sides by 7.

Is 217 the correct value of x? Take the original equation and replace x with 217. x

7

^31 becomes

217

7

 31 , which is true. The solution of 217 is correct.

With those four steps, you can tackle many different equations. You’ll encounter equations that

look much more complicated, but all that’s necessary is to apply these simple steps one after

another.

x

x

x

7

31

7

7317

217







CHECK POINT

Solve each equation.

1. x + 17 = 53


2. t – 11 = 46


3. -9a = 117
   4. y
   6

5 - 14

5. x + 14 = -3

Solving Two-Step Equations

In each of the examples we’ve looked at, just one bit of arithmetic had been done to the variable,

and so only one step was necessary to isolate the variable. More often, equations have more

than one step. The key to solving two-step equations is performing the correct operations in the

correct order.

Remember that the variable stands for a number. Imagine that you pick a number and then

perform some arithmetic with that number. You would follow the order of operations, and you’d

get an answer. The equation would show what you did and the answer you got. For example, if

you picked a number, multiplied it by 7 and then added 5, and got an answer of 26, the equation

would be 7x + 5 = 26.