how would I solve for (2x-3/2)= (-x-1/4)
add x to each side
add 3/2 to each side
I am not sure you mean what you typed.
do you perhaps mean
(2 x)^(-3/2) = (-x)^(-1/4) ???
If I am guessing right then
1/(2 x)^(+3/2) = 1/(-x)^(1/4)
then
(2 x)^(+3/2) = (-x)^(1/4)
square both sides for starters
(2x)^3 = (-x)^(1/2)
8 x^3 = (-x)^1/2+
well, square both sides again
64 x^6 = -x
or
64 x^5 = -1
x = (-1/64)^(1/5)
To solve for the variable x in the equation (2x - 3/2) = (-x - 1/4), you can follow these steps:
Step 1: Combine like terms
Start by simplifying both sides of the equation by combining like terms.
On the left side, multiply 2 with x and then subtract 3/2:
2x - 3/2 = -x - 1/4
Now we have:
(2x - 3/2) = (-x - 1/4)
Step 2: Isolate the x term
To isolate the variable x, we need to get rid of the terms with x on the right side of the equation.
We can achieve this by adding x to both sides of the equation:
(2x - 3/2) + x = (-x - 1/4) + x
Simplify the equation:
2x + x - 3/2 = -1/4
Combine like terms:
3x - 3/2 = -1/4
Step 3: Get rid of the fractions
To eliminate the fractions, we can multiply both sides of the equation by the least common denominator (LCD) of the fractions, which is 4.
Multiply both sides of the equation by 4:
4(3x - 3/2) = 4(-1/4)
Simplify the equation:
12x - 6 = -1
Step 4: Solve for x
Now that we have eliminated the fractions, we can solve for x. Start by adding 6 to both sides of the equation:
12x - 6 + 6 = -1 + 6
Simplify the equation:
12x = 5
Finally, divide both sides of the equation by 12 to solve for x:
12x/12 = 5/12
Simplify the equation:
x = 5/12
Therefore, the solution to the equation (2x - 3/2) = (-x - 1/4) is x = 5/12.