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Other Algebra Lessons

In this lesson, we will look into solving equations that have a term with the variable on both sides of the equation.

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

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

Examples:

1) 5*x* + 8 = 7*x*

2) 4*w* + 8 = 6*w* – 4

3) 6(*g* + 3) = – 2(*g* + 31)
**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) 2*x* + 7 = 4*x* – 7

2) 3*x* + 19 = 3 – 5*x*
**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 – 7*x*

2) 5*y* – 2 = 28 – *y*

3) 3 + 5*m* = 8*m*
– 9

4) 4 + 3*x* – 6 = 3*x* + 2 – *x*
**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

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Other Algebra Lessons

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 = –2*x* + 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 = –2*x* + 3

* Solution: *

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

* x* – 6 = –2*x* + 3

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

**Step 2:** Combine like terms

2*x* + *x *= 3 + 6

3*x* = 9

**Step 3:** Divide or multiply to isolate the variable

3*x* = 9 (Divide by 3)

*x* = 3

* Check: *

* x* – 6 = –2*x* + 3

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

–3 = –3

* Example: *

Consider the equation 6*x* – 4 = 3*x* + 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 6*x* – 4 = 3*x* + 2

* Solution: *

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

6*x* – 4 = 3*x* + 2

6*x* – 4 – 3*x *+ 4 = 3*x* + 2 – 3*x *+ 4 (Subtract 3*x* & add 4 to both sides)

**Step 2:** Combine like terms

6*x* – 3*x *= 2 + 4

3*x* = 6

**Step 3:** Divide or multiply to isolate the variable

3*x* = 6 (Divide by 3)

*x* = 2

* Check: *

6*x* – 4 = 3*x* + 2 (substitute *x* = 2 into the original equation)

6 • 2 – 4 = 3 • 2 + 2

8 = 8

Examples:

1) 5

2) 4

3) 6(

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) 2

2) 3

This requested video looks at solving equations with variables on both sides. It includes four examples.

Examples:

1)

2) 5

3) 3 + 5

4) 4 + 3

Examples:

1) 3(

2)

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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