Solving the Equation 10(1/2x+2)-5=3(x-6)+1
Introduction
In this article, we will solve the equation 10(1/2x+2)-5=3(x-6)+1 step by step. This equation involves variables, fractions, and integers, making it a challenging problem to solve. But don't worry, we'll break it down into manageable parts and solve it together.
Step 1: Simplify the Equation
First, let's simplify the equation by evaluating the expressions inside the parentheses.
10(1/2x+2) = 10(1/2x) + 10(2) = 5x + 20
And,
3(x-6) = 3x - 18
Now, rewrite the equation:
5x + 20 - 5 = 3x - 18 + 1
Step 2: Combine Like Terms
Combine like terms on both sides of the equation.
5x + 15 = 3x - 17
Step 3: Isolate the Variable
Subtract 3x from both sides to isolate the variable x.
2x + 15 = -17
Subtract 15 from both sides.
2x = -32
Divide both sides by 2.
x = -16
Solution
The value of x is -16.
Therefore, the solution to the equation 10(1/2x+2)-5=3(x-6)+1 is x = -16.
I hope this step-by-step solution helps you understand how to solve equations with variables, fractions, and integers.