Question

2/3(1/3x-1/2)=4x+2 1/2

Answer 1

2/3 * (1/3x - 1/2) = 4x + 2 1/2

2/9 x - 1/3 = 4x + 2,5 | * 9

2x - 3 = 36x + 22,5

-25,5 = 34x

x = -25,5/34

x = - 3/4

x = - 0,75

Answer 2

To solve the equation, we need to find the value of x. Let's start by simplifying the left-hand side of the equation:

2/3 * (1/3x - 1/2) = 4x + 2 1/2

Step 1: Distribute the 2/3 across the parentheses: (2/3) * (1/3x) - (2/3) * (1/2) = 4x + 2 1/2

Step 2: Simplify the expression within the parentheses: 2/9x - 1/3 = 4x + 2 1/2

Next, let's isolate the terms with x on one side of the equation. We'll move all the terms involving x to the left side and the constant terms to the right side:

Step 3: Move 4x to the left side by subtracting 4x from both sides: 2/9x - 4x - 1/3 = 2 1/2

Step 4: Move -1/3 to the left side by adding 1/3 to both sides: 2/9x - 4x = 2 1/2 + 1/3

Now, let's find a common denominator for the terms on the right side, which is 6:

Step 5: Convert 2 1/2 to an improper fraction: 2 1/2 = 2 + 1/2 = 2 + 3/6 = 12/6 + 3/6 = 15/6

Step 6: Combine the fractions on the right side: 2/9x - 4x = 15/6 + 1/3

Step 7: Find a common denominator for the fractions on the right side, which is 6: 2/9x - 4x = (15/6) * (2/2) + 2/6

Step 8: Simplify the right side: 2/9x - 4x = 30/12 + 2/6

Step 9: Combine the fractions on the right side: 2/9x - 4x = (30 + 4) / 12

Step 10: Combine the terms on the right side: 2/9x - 4x = 34/12

Now, let's continue solving for x:

Step 11: Find a common denominator for the left side, which is 9: (2/9x) * (9/9) - 4x = 34/12

Step 12: Simplify the left side: 2x - 4x = 34/12

Step 13: Combine the terms on the left side: -2x = 34/12

Step 14: Divide both sides by -2 to solve for x: x = (34/12) / -2

Step 15: Simplify the right side: x = 17/12

So, the value of x that satisfies the equation is x = 17/12.