Solving Two-Step Equations

Concept

Equations that can be solved in exactly two steps and gives the final value of the variable in two steps are called two step equations and are algebraic equations. These equations are just a little complicated than the one step equations. While solving a two step equation, we need to perform the operation on both sides of the equal to sign. Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers.

Rules

The general two steps to solve two step equations are:

Step 1: Eliminate the constant by performing the inverse operation of addition or subtraction to both sides of the equation.

Step 2: Simplify

Step 3: Eliminate the coefficient by performing the inverse operation of multiplication or division on both sides of the equation.

Step 4: Simplify. The remaining equation is the solution to the equation.

Step 5: Check the solution by substituting the found value of the variable into the original equation and simplifying to see if the equality is true.

Example

Solve the equation for ‘j’
-7j – 2 = – 37

Solution

To solve for j, “undo” each operation in the reverse order.

– 7j – 2 = – 37

– 7j – 2 + (2) = – 37 + (2) Add 2 to each side

– 7j = – 35 Simplify.

$\fn_phv \frac{-7}{-7}j =\frac{-35}{-7}$ Divide each side by – 7

j = 5 Simplify.

Practice Solving Two-Step Equations

Practice Problem 1

Solve the equation for ‘w’.
12w – 21 = 15

Practice Problem 2

Solve the equation for “b”.
Write the answer as a whole number or a fraction in simplest form.
$\fn_phv \frac{2}{7}b-5=4$

Practice Problem 3

Select the correct equation and solve it to answer the question.
While Cairo was on vacation, he rented a bicycle. He knows that the shop charged $12.50 plus an hourly rate. Suppose he had the bike for 6 hours and paid $41 for the rental. What was the hourly rate?