Linear equations is important math topic and occur frequently in most of the other maths topics and their applications in accountancy, engineering and physics. First we have to understand, what is a linear equation? A linear equation in one variable is an algebraic equation with one variable. It always makes a straight line when on a coordinate system. It can be written in the form ax+b=0 where a $\neq$0 and a and b are real numbers. In this section we have listed a list of questions for practice along with the solution of some of the questions. As Practice is very important to get master on the math problems, without practice and lack of concept knowledge no matter how long you have been trying nothing could be learnt. We provide detailed explanations for all the questions on linear equations. Practice below questions and excel your knowledge.

Linear equations with one variable have one of the below listed solutions:

Solution Type | Explanation | Example |

Identity | Solution set for these type of equations consists of all values which make the equation true | 4x = x + 3x or 4x = 4x Above equation is true for all x values |

Conditional | Such equations are true for only selected variable values | x + 2 = 2x - 4 => x - 2x = -4 - 2 => -x = -6 or x = 6 Only solution for the problem |

Inconsistent | Leads to a false statement | 2x - 3 = 2(x - 5) => 2x - 3 = 2x - 10 => -3 = -10 Which is not true. -3 $\neq$ -10 |

$\frac{y}{4}$ + 7 = 14

$\frac{y}{4}$ + 7 - 7 = 14 - 7

$\frac{y}{4}$ = 7

$\frac{y}{4}$ $\times$ 4 = 7 $\times$ 4

y = 28. Answer!

**Example 2**: Simplify 15y - 2 = $\frac{y}{2}$ + 3

Add 2 to both sides

15y - 2 + 2 = $\frac{y}{2}$ + 3 + 2

15y = $\frac{y}{2}$ + 5

Multiply both sides by 2

15y $\times$ 2 = 2($\frac{y}{2}$ + 5)

30 y = y + 10

Subtract y from both the sides

30 y - y = y + 10 - y

29 y = 10

Divide each side by 29 to isolate y, we get

29y/29 = 10/29

or y = 10/29

**Example 3**: Solve 10x - 1 = 3(12 + x) - 1

Solution: 10x - 1 = 3(12 + x) - 1

Expand the brackets

10x - 1 = 36 + 3x - 1

Combine like terms each side

10x -1 = 35 + 3x

Add 1 to both sides

10x -1 + 1 = 35 + 3x + 1

10x = 36 + 3x

Subtract 3x from both the sides

10x - 3x = 18 + 3x - 3x

7x = 36

Divide by 7 to find the value of x

7x/7 = 36 / 7

x = 36/7

Solution: 10x - 1 = 3(12 + x) - 1

Expand the brackets

10x - 1 = 36 + 3x - 1

Combine like terms each side

10x -1 = 35 + 3x

Add 1 to both sides

10x -1 + 1 = 35 + 3x + 1

10x = 36 + 3x

Subtract 3x from both the sides

10x - 3x = 18 + 3x - 3x

7x = 36

Divide by 7 to find the value of x

7x/7 = 36 / 7

x = 36/7

12m + m - 2 = 2m + 4 + 11 (Expand 2(m+2))

13m - 2 = 2m + 15

Add 2 to both the sides, we get

13m - 2 + 2 = 2m + 15 + 2

Simplify

13m = 2m + 17

Subtract 2m from both sides

13m - 2m = 2m + 17 - 2m

11m = 17

Divide by 11 both sides

11m/11 = 17/11

or m = 17/11