# Using two steps to solve an equation with whole numbers

#### Differential Equations

46 Lectures 2.5 hours

#### Linear Equations in Two Variables

9 Lectures 2.5 hours

When we solve an equation, we are solving to find the number that is missing. This missing number is usually represented by a letter. We find the value of that letter or variable to solve the equation.

Rules for Solving 2-Step Equations:

• Identify the variable.

We look for the letter in the problem. The variable letter can be any letter, not just x and y

2x + 3 = 7, x is the variable; 5w – 9 = 17, w is the variable

To solve the equation, we need to isolate the variable or get the variable by itself.

• Add/Subtract whole numbers so they’re all on one side.

For example, in the equation 4x – 7 = 21, we add 7 to both sides to get the whole numbers all on one’s side.

4x – 7 + 7 = 21 + 7; \: So 4x = 28

• Multiply /Divide to get the variable by itself.

For example, 4x = 28; Here we divide both sides of the equation by 4

$\frac{4x}{4} = \frac{28}{4}; \: x = 7$

• We check our work

We plug the value of the variable got as solution in the equation to check our work as follows.

Given equation is 4x – 7 = 21; we plug in the solution

x = 7

(4 × 7) – 7 = 21

28 – 7 = 21

21 = 21

So, the solution is verified to be correct.

Solve the following two step equation:

7g + 3 = 24

### Solution

Step 1:

We first identify the variable in the given equation

7g + 3 = 24

The only letter in the equation is g and it is the variable.

Step 2:

We add/subtract whole numbers to the equation so all are one side.

Here we subtract 3 from both sides of the equation.

7g + 3 – 3 = 24 – 3;

7g = 21

Step 3:

We multiply/divide on both sides of the equation to get the variable by itself

We divide both sides of the equation by 7

$\frac{7g}{7} = \frac{21}{7}$

g = 3

So, the solution of the equation is g = 3

Step 4:

We check our work by plugging the numbers into the equation.

Here, we plug g = 3 in the equation, 7g + 3 = 24

7 × 3 + 3 = 24

21 + 3 = 24

So the solution is verified to be correct.