To solve the equation 5/8(x−12)=10 , the first step is to reverse the multiplication. What number should both sides be divided by?(1 point)
To reverse the multiplication, we need to divide both sides of the equation by the coefficient of x, which is 5/8.
To reverse the multiplication, the first step is to isolate the term with the variable by dividing both sides of the equation by the coefficient of the variable.
In this case, the coefficient of the variable is 5/8.
To divide both sides by 5/8, we multiply both sides of the equation by the reciprocal of 5/8, which is 8/5.
So, the number that both sides of the equation should be divided by is 8/5.
To solve the equation 5/8(x−12)=10, the first step is indeed to reverse the multiplication by dividing both sides by the coefficient of the term containing the variable. In this case, the coefficient is 5/8.
To find the number that both sides should be divided by, we need to find the reciprocal of 5/8. The reciprocal of a fraction is obtained by flipping the numerator and the denominator. In this case, the reciprocal of 5/8 is 8/5.
So, both sides of the equation should be divided by 8/5. Performing this division will eliminate the fraction on the left side and isolate the variable on the left side of the equation. The equation becomes:
[(5/8) ÷ (8/5)](x − 12) = 10 ÷ (8/5)
To divide by a fraction, we can multiply by its reciprocal. So, we can rewrite the equation as:
(x − 12) = 10 ÷ (8/5) * (5/8)
Simplifying the right side, we have:
(x − 12) = (10 * 5) / (8 * 8/5)
(x − 12) = 50 / (64/5)
Now, to divide by a fraction, we can multiply by its reciprocal, so:
(x − 12) = 50 * (5/64)
(x − 12) = 250 / 64
Now that we have isolated the variable on the left side, we can proceed with solving the equation. However, to find the specific value of x, further simplification or manipulation may be required.