Final answer:
To solve the equation 3/5(x-7/10) = -3 1/4 for x, we first convert the mixed number to an improper fraction, perform basic algebraic operations to isolate x, and then simplify the resulting fraction. The solution to the equation is x = -29/6.
Step-by-step explanation:
To solve the mathematical problem completely where we have the equation 3/5(x-7/10) = -3 1/4, we begin by simplifying the given equation. Convert -3 1/4 to an improper fraction. This is equivalent to -13/4.
Now, let's multiply both sides of the equation by 5/3 to isolate the term with x:
5/3 * 3/5(x-7/10) = 5/3 * -13/4
The left-hand side simplifies to x-7/10, and for the right-hand side, we simplify by multiplying numerators and denominators:
x - 7/10 = -(13*5)/(4*3)
x - 7/10 = -65/12
Next, add 7/10 (which is the same as 21/30 or 7/12 in this case) to both sides:
x = -65/12 + 7/12
x = (-65 + 7) / 12
x = -58/12
Finally, simplify the fraction (if it's simplifiable) to get the value of x.
x = -29/6
Therefore, the value of x is -29/6.