What is the solution of the equation 8/5x = - 10?
A. -1/16
B. -16
C. -25/4
D. -5/8
To solve the equation (8/5)x = -10, we need to isolate x.
First, we can multiply both sides of the equation by the reciprocal of 8/5, which is 5/8, to cancel out the fraction on the left side:
(8/5)x * (5/8) = -10 * (5/8)
x = -50/8
Simplifying the right side of the equation:
x = -25/4
Therefore, the solution to the equation 8/5x = -10 is x = -25/4, which is option C.
To solve the equation 8/5x = -10, we can start by multiplying both sides of the equation by 5/8 to eliminate the fraction.
(5/8) * (8/5x) = (5/8) * (-10)
The 8/5 cancels out on the left side, and we are left with:
1x = (-50/8)
Next, we simplify the right side:
x = (-50/8)
The fraction can be simplified further. Both -50 and 8 are divisible by 2:
x = (-25/4)
Therefore, the solution for the equation 8/5x = -10 is C. -25/4.
To find the solution of the equation 8/5x = -10, we can follow these steps:
Step 1: Begin by multiplying both sides of the equation by the denominator, which in this case is 5. This will help eliminate the fraction.
(8/5)x * 5 = -10 * 5
Simplifying the expression, we get:
(8/5) * 5 * x = -10 * 5
Step 2: Simplify both sides of the equation.
(8/5) * 5 = 8, so the equation becomes:
8x = -50
Step 3: Solve for x by dividing both sides of the equation by the coefficient of x, which in this case is 8.
8x / 8 = -50 / 8
Simplifying, we have:
x = -50 / 8
Step 4: Further simplify the result.
-50 / 8 can be reduced by dividing both the numerator and denominator by their greatest common divisor, which is 2.
-50 / 8 = (-25 * 2) / (4 * 2) = -25 / 4
So, the solution to the equation 8/5x = -10 is x = -25/4.
Therefore, the correct option is C. -25/4.