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

Related Topics:

Other Algebra Lessons

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.

* Example: *

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

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.

* Example: *

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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