10(1/2x+2)-5=3(x-6)+1

2 min read Jun 20, 2024

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.