Question

Solve the following equation 2/3x+6=1/2x+1/4x​

Answer 1

The solution to the equation 2/3x + 6 = 1/2x + 1/4x is found by combining like terms and using common denominators. After simplifying, it is determined that x = 72.

Step-by-step explanation:

To solve the equation 2/3x + 6 = 1/2x + 1/4x, we first need to combine like terms. The terms 1/2x and 1/4x on the right side of the equation are like terms because they both contain the variable 'x'. To combine them, we convert them to a common denominator.

Putting 1/2 and 1/4 to a common denominator gives us 2/4 + 1/4, which equals 3/4. So, the equation becomes 2/3x + 6 = 3/4x. Next, to isolate the x terms on one side of the equation, we subtract 2/3x from both sides, which gives:

6 = 3/4x - 2/3x

Using common denominator for 3/4 and 2/3 gives us 9/12x - 8/12x, which simplifies to 1/12x. So now we have:

6 = 1/12x

Multiply both sides by 12 to solve for x:

72 = x

Therefore, the solution to the equation 2/3x + 6 = 1/2x + 1/4x is x = 72.

Answer 2

x = -72/17

Step-by-step explanation:

(2/3)*x+(1/2)*x+(1/4)*x+6 = 0

17/12*x+6 = 0 // - 6

17/12*x = -6 // : 17/12

x = -6/17/12

x = -72/17

x = -72/17