Solve 3/2*(3/4x)+1/2x=5/2*(frac{3}{4}x)+40

$$\frac{ 3 }{ 2 } \times ( \frac{ 3 }{ 4 } x)+ \frac{ 1 }{ 2 } x= \frac{ 5 }{ 2 } \times ( \frac{ 3 }{ 4 } x)+40$$

Solve for x

$$x=-160$$

Steps for Solving Linear Equation

Multiply \frac{3}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 3}{2\times 4}x+\frac{1}{2}x=\frac{5}{2}\times \frac{3}{4}x+40$$

Do the multiplications in the fraction \frac{3\times 3}{2\times 4}.

$$\frac{9}{8}x+\frac{1}{2}x=\frac{5}{2}\times \frac{3}{4}x+40$$

Combine \frac{9}{8}x and \frac{1}{2}x to get \frac{13}{8}x.

$$\frac{13}{8}x=\frac{5}{2}\times \frac{3}{4}x+40$$

Multiply \frac{5}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{8}x=\frac{5\times 3}{2\times 4}x+40$$

Do the multiplications in the fraction \frac{5\times 3}{2\times 4}.

$$\frac{13}{8}x=\frac{15}{8}x+40$$

Subtract \frac{15}{8}x from both sides.

$$\frac{13}{8}x-\frac{15}{8}x=40$$

Combine \frac{13}{8}x and -\frac{15}{8}x to get -\frac{1}{4}x.

$$-\frac{1}{4}x=40$$

Multiply both sides by -4, the reciprocal of -\frac{1}{4}.

$$x=40\left(-4\right)$$

Multiply 40 and -4 to get -160.

$$x=-160$$