Answer: x = 87/68.
Explanation:
To solve the equation using the distributive property, we need to distribute the fraction 17/3 to both terms inside the parentheses.
First, distribute 17/3 to x: (17/3) * x = 17x/3
Next, distribute 17/3 to -3/2: (17/3) * (-3/2) = -51/6
The equation becomes:
17x/3 - 51/6 = -5/4
To simplify the equation, let's find a common denominator for the fractions involved. The least common denominator (LCD) for 3, 6, and 4 is 12.
Multiplying both sides of the equation by 12 to clear the denominators, we get:
12 * (17x/3) - 12 * (51/6) = 12 * (-5/4)
This simplifies to:
68x - 102 = -15
To isolate x, let's move the constant term (-102) to the other side of the equation by adding 102 to both sides:
68x - 102 + 102 = -15 + 102
This simplifies to:
68x = 87
Finally, we can solve for x by dividing both sides of the equation by 68:
(68x)/68 = 87/68
x = 87/68
Therefore, the solution to the equation is x = 87/68.
(hope this helps!)