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 distribute 5/8 to the terms inside the parentheses:
5/8 (x - 1/2) = 10
(5/8)(x) - (5/8)(1/2) = 10
5/8 x - 5/16 = 10
After distributing, the next step is to reverse the multiplication by dividing both sides of the equation by 5/8.
So, both sides should be divided by 5/8.
To reverse the multiplication in the equation "5/8 (x - 1/2) = 10", you need to divide both sides by the coefficient of the term being multiplied. In this case, the coefficient is 5/8.
Therefore, to isolate the variable x, both sides of the equation should be divided by 5/8.
To reverse the multiplication in the equation 5/8 (x - 1/2) = 10, we need to divide both sides of the equation by the coefficient of the variable term, which is 5/8.
To divide both sides by 5/8, we can multiply both sides of the equation by the reciprocal of 5/8, which is 8/5.
So, dividing both sides by 5/8 is equivalent to multiplying both sides by 8/5.
Let's perform the calculation:
(5/8) * (x - 1/2) = 10
Multiplying both sides of the equation by 8/5:
[(5/8) * (x - 1/2)] * (8/5) = 10 * (8/5)
On the left-hand side, the (8/5) terms cancel out:
[(5/8) * (x - 1/2)] * (8/5) = x - 1/2
So, the equation becomes:
x - 1/2 = (10 * 8/5)
Now, we can simplify the right-hand side:
x - 1/2 = 80/5
Next, we can add 1/2 to both sides of the equation to isolate the variable x:
x - 1/2 + 1/2 = 80/5 + 1/2
On the left-hand side, the (1/2) terms cancel out:
x = 80/5 + 1/2
To add the fractions, we need to find a common denominator, which is 10:
x = (80/5) + (1/2) * (2/2)
Rewriting 1/2 as an equivalent fraction with a denominator of 10:
x = 80/5 + 2/10
Now, all the fractions have the same denominator, so we can add them:
x = (80 + 2) / 5
x = 82/5
Therefore, the solution to the equation 5/8 (x - 1/2) = 10 is x = 82/5.