__Objective__

At the end of the lesson, students should be able to solve equations with the variable on both sides.

Sometimes, the unknown quantity will appear on both sides of an equation.

The first step in solving an equation with a variable on both sides is to **get the variable on one side**. This is done by reversing the addition or subtraction of one of the terms with the variable. In other words, we must add to both sides or subtract from both sides one of the quantities that contains the variable. It is generally easier to add or to subtract the smaller quantity from the larger quantity, so that we work with positive coefficients. Once the variable is on one side only, we can proceed using inverse operations.

__Example 1__

Solve for x:

a) 4x=2x+16 b) 3x + 2x = 12 – x c) 5*x* = 6 + 2*x*

__Solution__

b) 3x + 2x = 12 – x

3x + 2x = 12 – x **Simplify. **

5x = 12 – x **Add x left sides ****to get the variable on one side.**

5x + x = 12 **Simplify. **

6x = 12 **Divide by 6 on both sides.**

x = **2**

c)5*x* = 6 + 2*x* **Subtract -2x from both sides.**

5*x* – 2*x* = 6 + 2*x* – 2*x* **Simplify. **

3*x* = 6 **Divide by 6 on both sides.**

x=**2**

**Check: 3(2) + 2(2) = 12 – 2**

** 6+4=10 **

** 10=10**

__Example 2__

Solve for the unknown in the following:

a) 5*y*– 3 = 3*y*+ 5 b) 12k+15 = 35+2k c) 2x–6 = 5x+18

__Solution __

a)5y – 3 – 3y = 3y + 5 – 3y **Simplify. **

2y – 3 = 5 **Add 3 ****to both one side**

2*y* – 3 + 3 = 5 + 3

2y = 8** Divide by 2 on both sides.**

y= **4**

**Check: 5(4) – 3 = 3(4) + 5 **

** 20-3 = 12+5**

** 17 = 17**

b) 12k+15=35+2k

**Check: 2(–8) – 6 = 5(–8) + 18**

** –16 – 6 = –40 + 18**

** –22 =–22**

** **__Example 3__

Solve the equation: 2x + 3 = 6 − (2x − 3).

__Solution __

2x + 3 = 6 − (2x − 3)

**Expand to remove the brackets on the right side.**

2x + 3 = 6 − 2x + 3 ** group like terms**

2x+2x =6 +3 ** -3 ** **Simplify.**

4x = 6 ** Divide both sides by 4.**

4x/4 = 6/4

x=**1.5**

**Check: 2(1.5) +3=6− (2(1.5)− 3) **

** 3+3=6 −(3−3)**

** 6=6−0**

** 6=6 **

Login

Accessing this unit requires a login, please enter your credentials below!