- Equations and Applications
- Home
- Additive property of equality with decimals
- Multiplicative property of equality with decimals
- Multiplicative property of equality with whole numbers: Fractional answers
- Multiplicative property of equality with fractions
- Using two steps to solve an equation with whole numbers
- Solving an equation with parentheses
- Solving a fraction word problem using a linear equation of the form Ax = B
- Translating a sentence into a multi-step equation

# Using two steps to solve an equation with whole numbers

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.