Solving an equation
Initial explanation
We want to find which value must have x, so this equation is true:
13x - 2(8 + 5x) = 12 - 11x
In order to solve the equation for x we want to "leave it alone" on one side.
In order to do that we just have to remember one simple rule:
Before we start we are going to work with the most simple "version" of the equation.
Step 1: simplifying the equation
We want to simplify by taking off the parenthesis:
-2(8+5x) = -2 · 8 -2 · 5x
= -16 -10x
Then
13x - 2(8 + 5x) = 12 - 11x
↓
13x -16 -10x = 12 - 11x
Step 2: simplifying the equation
Since 13x - 10x = 3x, then
13x -16 -10x = 12 - 11x
↓
3x - 16 = 12 - 11x
Step 3: taking the terms with x to the left side
We want to take 11x to the left:
3x - 16 = 12 - 11x
↓ adding 11x both sides
3x - 16 + 11x = 12 - 11x + 11x
3x + 11x - 16 = 12
↓ since 3x + 11x = 14x
14x - 16 = 12
Step 4: taking the terms without x to the right side
We want to take -16 to the right:
14x - 16 = 12
↓
14x = 12 + 16
↓ since 12 + 16 = 28
14x = 28
Step 5: "leaving x alone"
We want to take the 14 to the right:
14x = 28
↓
x = 28/14 = 2
Answer: x = 2