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

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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

The following video shows more examples of solving equations with variables on both sides of the equation.

5*x* + 8 = 7*x*

4*w* + 8 = 6*w* – 4

6(*g* + 3) = – 2(*g* + 31)

Solving Equations with Variables on Both Sides.

2*x* + 7 = 4*x* – 7

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.

5

3 + 5

4 + 3

Equations with Variables on Both Sides

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