Solve the following equation using the distributive property

17/3(x-3/2)=-5/4

1 answer

To solve the equation we will apply the distributive property by multiplying 17/3 by each term in the parentheses:

17/3(x) - 17/3(3/2) = -5/4

This simplifies to:

17/3x - 51/6 = -5/4

Now we will simplify the fractions:

x(17/3) - 17/2 = -5/4

Next, we need to find a common denominator for both fractions:

x(17/3) - (17/2)(2/2) = -5/4

This simplifies to:

17x/3 - 34/4 = -5/4

Now, let's combine the fractions:

17x/3 - 17/2 = -5/4

To further simplify, let's find a common denominator for the fractions:

17x/3 - (17/2)(3/3) = -5/4

This simplifies to:

17x/3 - 51/6 = -5/4

Now, we can add 51/6 to both sides to isolate the x term:

17x/3 = -5/4 + 51/6

To find a common denominator for the fractions:

17x/3 = -15/12 + 102/12

This simplifies to:

17x/3 = 87/12

Now, we can multiply both sides by 3 to cancel out the fraction on the left side:

17x = 87/12 * 3

Next, let's simplify the fraction on the right side:

17x = 261/12

Now, divide both sides by 17 to solve for x:

x = (261/12) / 17

Finally, we can simplify the fraction on the right side:

x = 261/12 รท 17
x = 15.3529

Therefore, the solution to the equation is x = 15.3529.