solve the equation
the quantity z plus 3 divided by 5 minus one fourth equals three fourths
To solve the equation, we can write the given equation in mathematical notation as follows:
(z + 3)/5 - 1/4 = 3/4
To get rid of the fractions, we can multiply both sides of the equation by the least common denominator (LCD), which in this case is 20. This will result in:
20((z + 3)/5) - 20(1/4) = 20(3/4)
After simplifying, we have:
4(z + 3) - 5 = 15
Next, distribute the 4 on the left side by multiplying it to (z + 3):
4z + 12 - 5 = 15
Combine like terms:
4z + 7 = 15
Subtract 7 from both sides:
4z = 8
Divide both sides by 4:
z = 2
Therefore, the solution to the equation is z = 2.