Solving Equations With Variables On Both Sides

The following figure shows how to solve equations with variables on both sides. Scroll down the page for more examples and solutions.

Example:
Consider the equation x – 6 = –2x + 3.
To isolate the variable, we need to get all the variable terms to one side and the constant terms to the other side. Next, we combine like terms and then isolate the variable by multiplying or dividing.

Solve x – 6 = –2x + 3

Solution:
Step 1: Get all the variable terms to one side and the constant terms to the other side.

x – 6 = –2x + 3
x – 6 + 2x + 6 = –2x + 3 + 2x + 6 (Add 2x & 6 to both sides)

Step 2: Combine like terms
2x + x = 3 + 6
3x = 9

Step 3: Divide or multiply to isolate the variable
3x = 9 (Divide by 3)
x = 3

Check:
x – 6 = –2x + 3
3 – 6 = –2 • 3 + 3 (substitute x = 3 into the original equation)
–3 = –3

Example:
Consider the equation 6x – 4 = 3x + 2. To isolate the variable, we need to get all the variable terms to one side and the constant terms to the other side. Next, we combine like terms and then isolate the variable by multiplying or dividing.

Solve 6x – 4 = 3x + 2

Solution:
Step 1: Get all the variable terms to one side and the constant terms to the other side.
6x – 4 = 3x + 2
6x – 4 – 3x + 4 = 3x + 2 – 3x + 4 (Subtract 3x & add 4 to both sides)

Step 2: Combine like terms
6x – 3x = 2 + 4
3x = 6

Step 3: Divide or multiply to isolate the variable
3x = 6 (Divide by 3)
x = 2

Check:
6x – 4 = 3x + 2 (substitute x = 2 into the original equation)
6 • 2 – 4 = 3 • 2 + 2
8 = 8

How to solve equations with variables on both sides of the equation?
Examples:

1. 5x + 8 = 7x
2. 4w + 8 = 6w – 4
3. 6(g + 3) = – 2(g + 31)

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Solving Equations with Variables on Both Sides
Step 1: Add and subtract terms to get the variables on one side and the constants on the other.
Step 2: Multiply or divide to isolate the variable.

Examples:

1. 2x + 7 = 4x – 7
2. 3x + 19 = 3 – 5x

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Equations With Variables on Both Sides
This requested video looks at solving equations with variables on both sides. It includes four examples.
Examples:

1. x + 14.8 = 102 – 7x
2. 5y – 2 = 28 – y
3. 3 + 5m = 8m – 9
4. 4 + 3x – 6 = 3x + 2 – x

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How to use the distributive property to simplify equations with variables on both sides?
Examples:

1. 3(x – 1) = 2(x + 3)
2. z/6 = 2(z + 1)/9

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