## Solve algebra equations

**Introduction :**

An equation is a mathematical statement that asserts the equality of two expressions. Equations consist of the expressions that to be equal on opposite sides of an equal sign. (Source: From Wikipedia). The following rules are used to solve the equation and the equation does not change.

1) Add or subtract any variable or number to the both sides of the equation

2) Multiply or divide any variable or number to the both sides of the equation.

Examples of equation

**:**t+5=4+2t, s+5=1+5s, 4x+2=9+1x.

Now, we are going to see some of the problems on algebraic equations solve for the variables.

**Problems to solve algebra equations:**

**Example problem 1:**

Solve an equation for the variable m:

**6 m + 18 = 24**

**Solution:**

Subtract 18 on both sides of the equation

6m + 18 - 18 = 24 – 18

6

*m*= 6

Divide by 6 on both sides of the equation

`(6m) / 6 = 6 / 6`

x = 1

So, x = 1 is the solution of the given equation.

**Example problem 2:**

Solve an equation for the variable t:

**`(t / 2)` + 16 = 18**

**Solution:**

`(t / 2)` + 16 = 18

Subtract 16 on both sides of the equation

`(t / 2)` + 16 - 16 = 18 – 16

`(t / 2)` = 2

Multiply 2 on both sides of the equation

`(t / 2) ` * 2 = 2* 2

t = 4

So, t = 4 is the solution of the given equation.

**Few more problems to solve algebra equations:**

**Example problem 3:**

Find the value of x:

**-1 x + 10 = x + 20**

**Solution:**

Subtract x on both sides of the equation

-1 x + 10 - x = x + 20 - x

-2x + 10 = 20

Subtract 10 on both sides of the equation

-2

*x*+ 10 - 10 = 20 – 10

-2

*x*= 10

Divide by -2 on both sides of the equation

`(-2x) / -2 = 10 / -2`

x = -5

So, x = -5 is the solution of the given equation.

**Example problem 4:**

Find the value of t:

**4(x + 2) = 4**

**Solution:**

4(x + 2) = 4

4x + 8 = 4

Subtract 8 on both sides of the equation

4x + 8 - 8 = 4 – 8

4x = - 4

Divide by 4 on both sides of the equation

`(4x) / 4 = -4 / 4`

x = -1

So, t = -1 is the solution of the given equation.

**Practice problems to solve algebra equations:**

**1)**Solve an equation for the variable x:

**5x + 11 = 6**(Answer: x = -1)

2) Solve an equation for the variable m:

**4m + 10 = 26**(Answer: m = 4)