Linear Equations with one varable

An equation of the type ax + b = 0 , a is not equal to zero is called a linear equation in the variable x.

Example :solve for x , 2x + 5 = 10 - 3x
( bring x terms one side and numbers other side,when - 3x comes to left side it becoms +3x, +5 becomes - 5 when it comes to right side)
2x + 3x = 10-5
5x=5(divide both side by 5)
5x/5=5 / 5
x = 1

Practice:solve for x
8 x + 8 = 5 x + 19
5 x - 3 = 3 x - 5
4 p + 2 = 9 - 3 p

Answers:
x = 9
x = -1
p = 1

Example: Solve for x , 6x - 5 - 2x + 3 - 2 = 4
First, simplify the equation by combining like terms
(like terms are terms containing same literal example 2x , -7x ,8/7x)
4x - 4 = 4
4x - 4 + 4 = 4 + 4 ( adding 4 to both sides)
4x = 8
4x / 4 = 8 / 4 (dividing both sides by 4)
x = 2

Practice: solve for x
m + 13m - 13 = 15
7 = 8 + 5j – 9 + 3j
d + 8 - 14 + 14d = 39

Answers:
m = 2
j = 1
d = 3

Example: solve for x , ( 3 x - 1) – 2 ( x – 5 ) = 3 ( 5 – x )+ 6
(use distributive property, a(b+c) = a*b + a*c ), -2(x-5)= -2x+ 10 , 3(5-x)=15-3x
3 x – 1 - 2 x + 10 = 15 – 3 x + 6
3 x -2 x + 3 x = 15 + 6 + 1 – 10 (bring x terms to left side,numbers to right side)
4 x = 12 (combining like terms)
4x/ 4= 12/4 (dividing both side by 4)
x= 3

Practice:solve for x
2( x – 4 ) – 3 ( x + 2 ) = 4 ( x + 1 ) – 8
3( y - 7 ) - 2( 3y - 4 ) = ( 2- 5y )+ 3
7 – 3 (2x-1) = 4 (5 – x)- 7x

Answers:
x = -2
y = 2
x = 2