Solving the Equation: 6((x + 1)/8 - (2x - 3)/16) = 3(3/4 * x - 1/4) - 3/8 * (3x - 2)
In this article, we will solve the equation 6((x + 1)/8 - (2x - 3)/16) = 3(3/4 * x - 1/4) - 3/8 * (3x - 2). This equation involves fractions and variables, and we will use algebraic methods to simplify and solve it.
Step 1: Simplify the Left-Hand Side of the Equation
Let's start by simplifying the left-hand side of the equation:
6((x + 1)/8 - (2x - 3)/16)
= 6((x + 1)/8 - (2x/16 - 3/16))
= 6((x + 1)/8 - (x/8 - 3/16))
= 6((x/8 + 1/8) - (x/8 - 3/16))
= 6(x/8 + 1/8 - x/8 + 3/16)
= 6(1/8 + 3/16)
= 6(2/16 + 3/16)
= 6(5/16)
= 30/16
Step 2: Simplify the Right-Hand Side of the Equation
Now, let's simplify the right-hand side of the equation:
3(3/4 * x - 1/4) - 3/8 * (3x - 2)
= 3(3x/4 - 1/4) - 3/8 * (3x - 2)
= 9x/4 - 3/4 - 9x/8 + 6/8
= 9x/4 - 3/4 - 9x/8 + 6/8
= 18x/8 - 6/8 - 9x/8 + 6/8
= 18x/8 - 9x/8
= 9x/8
Step 3: Equate the Simplified Expressions
Now that we have simplified both sides of the equation, we can equate them:
30/16 = 9x/8
Step 4: Solve for x
To solve for x, we can multiply both sides of the equation by 8 to eliminate the fraction:
30 * 8/16 = 9x
240 = 9x
x = 240/9
x = 80/3
Therefore, the value of x is 80/3.
