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 solve the equation 5/8 (x - 1/2) = 10, the first step is to reverse the multiplication by multiplying both sides of the equation by the reciprocal of 5/8, which is 8/5.
When multiplying both sides of the equation by 8/5, we get:
8/5 * 5/8 (x - 1/2) = 10 * 8/5
This simplifies to:
1(x - 1/2) = 16/5
Now, the equation becomes:
x - 1/2 = 16/5.
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 by 5/8.
When dividing by a fraction, we can multiply both sides of the equation by the reciprocal (or multiplicative inverse) of that fraction. In this case, the reciprocal of 5/8 is 8/5, so we need to multiply both sides by 8/5 to cancel out the 5/8 on the left side.
By doing this, the left side simplifies and the equation becomes:
(x - 1/2) = 10 * (8/5)
Now, we can simplify the right side of the equation by multiplying 10 with 8/5:
(x - 1/2) = 80/5
The right side simplifies to:
(x - 1/2) = 16
Now the equation is simplified, and the next step would be to isolate the variable x by adding 1/2 to both sides of the equation.
To solve the equation 5/8 (x - 1/2) = 10, the first step is indeed to reverse the multiplication. Since the term on the left side of the equation is being multiplied by 5/8, we need to divide both sides by 5/8 to cancel out the multiplication.
To achieve this, we can multiply both sides of the equation by the reciprocal of 5/8, which is 8/5. Multiplying both sides by 8/5 will give us:
(8/5) * (5/8) * (x - 1/2) = (8/5) * 10
On the left side, the multiplication of 5/8 and 8/5 will cancel out and leave us with just (x - 1/2):
(x - 1/2) = (8/5) * 10
Simplifying the right side, we have:
(x - 1/2) = 80/5
(x - 1/2) = 16
Therefore, to solve the equation, both sides should be divided by 5/8, or multiplied by the reciprocal 8/5.