Solving a linear equation
We want to solve the equations:
1. 5x + 7 = x + 13
2. 2(x + 7) = -4x + 14
Step 1: removing parenthesis
We want to remove the parenthesis using the distributive property:
Equation 1: does not have
1. 5x + 7 = x + 13
↓
1. 5x + 7 = x + 13
Equation 2:
2. 2(x + 7) = -4x + 14
↓ distributive property
2(x + 7) = 2 · x + 2 · 7 = 2x + 14
↓
2. 2x + 14 = -4x + 14
Step 2: rearranging the equations
Rearranging the terms so the terms with the unkown variable x are on the left side and the other ones on the right side:
Equation 1:
1. 5x + 7 = x + 13
↓ substracting x both sides
5x + 7 - x = 13
↓ substracting 7 both sides
5x - x = 13 - 7
↓
1. 4x = 6
Equation 2:
2. 2x + 14 = -4x + 14
↓ adding 4x both sides
2x + 14 + 4x = 14
↓ substracting 14 both sides
2x + 4x = 14 - 14
↓
2. 6x = 0
Step 3: finding x
Solving the equation for x:
Equation 1:
1. 4x = 6
↓ dividing by 4 both sides
4x/4 = 6/4
↓
1. x = 1.5
Equation 2:
2. 6x = 0
↓ dividing by 6 both sides
6x/6 = 0/6
↓
2. x = 0
Answer: If 5x + 7 = x + 13 then x = 1.5. If 2(x + 7) = -4x+14 then x = 0