To solve the equation 5/8(x−1/2)=10 , the first step is to reverse the multiplication. What number should both sides be divided by?
To reverse the multiplication, we need to divide both sides of the equation by the coefficient in front of the variable (which is (5/8)).
So, both sides should be divided by (5/8).
To reverse the multiplication in the equation 5/8(x - 1/2) = 10, the first step is to multiply both sides by the reciprocal of 5/8, which is 8/5. This step is necessary to isolate the variable x and solve for its value.
To solve the equation 5/8(x-1/2) = 10, the first step is indeed to reverse the multiplication by dividing both sides of the equation. To determine the number that both sides should be divided by, you need to isolate the variable term by getting rid of any coefficient in front of it.
In this case, the variable term is (x-1/2), and its coefficient is 5/8. To get rid of this coefficient, you need to multiply both sides of the equation by the reciprocal (or multiplicative inverse) of 5/8. Since the reciprocal of a fraction is obtained by switching the numerator and denominator, the reciprocal of 5/8 is 8/5.
So, multiplying both sides of the equation by 8/5, we have:
(8/5) * (5/8) * (x - 1/2) = (8/5) * 10
The 5/8 and 8/5 cancel out on the left side, leaving us with:
1 * (x - 1/2) = (8/5) * 10
Simplifying further, we get:
x - 1/2 = 16
Finally, to isolate the variable x, add 1/2 to both sides of the equation:
x = 16 + 1/2
Simplifying the right side gives the solution:
x = 33/2, or x = 16.5