What is the solution of the equation 5/2x = −1/8?(1 point)
Responses
−2/0
negative 20
−1/20
negative Start Fraction 1 over 20 End Fraction
−5/16
negative Start Fraction 5 over 16 End Fraction
1/20
The correct solution of the equation 5/2x = −1/8 is -1/20.
To solve the equation 5/2x = -1/8, we need to isolate the variable x.
Step 1: Multiply both sides of the equation by the reciprocal of 5/2, which is 2/5.
2/5 * (5/2x) = 2/5 * (-1/8)
This simplifies to:
1/x = -2/40
Step 2: Simplify the right side of the equation.
1/x = -1/20
Therefore, the solution to the equation 5/2x = -1/8 is x = -1/20 (or negative Start Fraction 1 over 20 End Fraction).
To find the solution to the equation 5/2x = -1/8, you need to first isolate the variable x on one side of the equation.
Let's start by multiplying both sides of the equation by 2/5 to eliminate the fraction:
(2/5) * (5/2x) = (2/5) * (-1/8)
This simplifies to:
1/x = -2/40
Next, we can simplify the equation further by multiplying both sides by x to get rid of the denominator:
(1/x) * x = (-2/40) * x
The x on the left side cancels out, leaving us with:
1 = (-2/40) * x
Now, we can simplify the right side of the equation:
1 = -2x/40
To isolate x, we can cross multiply:
40 * 1 = -2x
This simplifies to:
40 = -2x
To solve for x, divide both sides of the equation by -2:
40/-2 = x
The equation reduces to:
-20 = x
So, the solution to the equation 5/2x = -1/8 is x = -20.