Question

17/3 (x - 3/2) = - 5/4
can you solve for x?

Answer 1

Answer:

$\boxed{x =\dfrac{87}{68}}$

Step-by-step explanation:

$\dfrac{17}{3} \left(x-\dfrac{3}{2} \right) = -\dfrac{5}{4}$

Using FOIL in LHS

$\dfrac{17}{3}x - \dfrac{17}{3} \cdot \dfrac{3}{2} = -\dfrac{5}{4}$

$\dfrac{17}{3}x - \dfrac{51}{6} = -\dfrac{5}{4}$

$\dfrac{17}{3}x = -\dfrac{5}{4}+ \dfrac{51}{6}$

$\dfrac{17}{3}x = -\dfrac{5(3)}{4(3)}+ \dfrac{51(2)}{6(2)}$

$\dfrac{17}{3}x = -\dfrac{15}{12}+ \dfrac{102}{12}$

Now the denominator of the fractions in the RHS are the same

$\dfrac{17}{3}x = \dfrac{87}{12}$

$x = \dfrac{87}{12} \cdot \dfrac{3}{17}$

$x =\dfrac{261}{204} = \dfrac{87}{68}$

$\boxed{x =\dfrac{87}{68}}$