Solving the Equation: (x-10) + (4x-10) = 90
This article will guide you through the steps to solve the equation (x-10) + (4x-10) = 90.
Step 1: Simplify the Equation
First, we need to combine like terms on the left side of the equation.
- x + 4x = 5x
- -10 - 10 = -20
Now the equation is: 5x - 20 = 90
Step 2: Isolate the Variable
To get 'x' by itself, we need to get rid of the '-20'. We can do this by adding 20 to both sides of the equation.
- 5x - 20 + 20 = 90 + 20
- 5x = 110
Step 3: Solve for x
Finally, we need to isolate 'x' by dividing both sides of the equation by 5.
- 5x / 5 = 110 / 5
- x = 22
Solution
Therefore, the solution to the equation (x-10) + (4x-10) = 90 is x = 22.
Verification
We can verify our solution by plugging 'x = 22' back into the original equation.
- (22 - 10) + (4 * 22 - 10) = 90
- 12 + 78 = 90
- 90 = 90
This confirms that our solution is correct.