Final answer:
To solve for x in the equation 5(x−3 3/4)=7 1/2, we need to isolate x on one side. By distributing the 5, combining like terms, and performing the necessary operations, we find that x is equal to 5 3/10.
Step-by-step explanation:
To solve for x, we need to isolate it on one side of the equation.
First, distribute the 5 into the parentheses: 5(x - 3 3/4) = 7 1/2
5x - 5(3 3/4) = 7 1/2
5x - 15 3/4 = 7 1/2
Next, combine like terms: -15 3/4 + 7 1/2 = -15 6/8 + 7 4/8 = -8 2/8 = -7 1/4
Now, add 7 1/4 to both sides: 5x - 7 1/4 = 7 1/2 + 7 1/4
5x - 7 1/4 = 14 3/4
Finally, divide both sides by 5 to isolate x: (5x - 7 1/4)/5 = (14 3/4)/5
x - 7 1/4/5 = 14 3/4/5
x - 1 7/20 = 2 19/20
Therefore, x = 1 7/20 + 2 19/20 = 4 26/20 = 5 6/20 = 5 3/10