Solve 3/4(4x/1-12/1)-5/3(frac{3}{2}x+frac{1}{1})

$$\frac { 3 } { 4 } ( \frac { 4 x } { 1 } - \frac { 12 } { 1 } ) - \frac { 5 } { 3 } ( \frac { 3 } { 2 } x + \frac { 1 } { 1 } )$$

Evaluate

$$\frac{x}{2}-\frac{32}{3}$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{3}{4}\left(\frac{4x}{1}-\frac{12}{1}\right)-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Anything divided by one gives itself.

$$\frac{3}{4}\left(4x-\frac{12}{1}\right)-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Anything divided by one gives itself.

$$\frac{3}{4}\left(4x-12\right)-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Use the distributive property to multiply \frac{3}{4} by 4x-12.

$$\frac{3}{4}\times 4x+\frac{3}{4}\left(-12\right)-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Cancel out 4 and 4.

$$3x+\frac{3}{4}\left(-12\right)-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Express \frac{3}{4}\left(-12\right) as a single fraction.

$$3x+\frac{3\left(-12\right)}{4}-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Multiply 3 and -12 to get -36.

$$3x+\frac{-36}{4}-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Divide -36 by 4 to get -9.

$$3x-9-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Use the distributive property to multiply -\frac{5}{3} by \frac{3}{2}x+1.

$$3x-9-\frac{5}{3}\times \frac{3}{2}x-\frac{5}{3}$$

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

$$3x-9+\frac{-5\times 3}{3\times 2}x-\frac{5}{3}$$

Cancel out 3 in both numerator and denominator.

$$3x-9+\frac{-5}{2}x-\frac{5}{3}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$3x-9-\frac{5}{2}x-\frac{5}{3}$$

Combine 3x and -\frac{5}{2}x to get \frac{1}{2}x.

$$\frac{1}{2}x-9-\frac{5}{3}$$

Convert -9 to fraction -\frac{27}{3}.

$$\frac{1}{2}x-\frac{27}{3}-\frac{5}{3}$$

Since -\frac{27}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x+\frac{-27-5}{3}$$

Subtract 5 from -27 to get -32.

$$\frac{1}{2}x-\frac{32}{3}$$

Expand

$$\frac{x}{2}-\frac{32}{3}$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{3}{4}\left(\frac{4x}{1}-\frac{12}{1}\right)-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Anything divided by one gives itself.

$$\frac{3}{4}\left(4x-\frac{12}{1}\right)-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Anything divided by one gives itself.

$$\frac{3}{4}\left(4x-12\right)-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Use the distributive property to multiply \frac{3}{4} by 4x-12.

$$\frac{3}{4}\times 4x+\frac{3}{4}\left(-12\right)-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Cancel out 4 and 4.

$$3x+\frac{3}{4}\left(-12\right)-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Express \frac{3}{4}\left(-12\right) as a single fraction.

$$3x+\frac{3\left(-12\right)}{4}-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Multiply 3 and -12 to get -36.

$$3x+\frac{-36}{4}-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Divide -36 by 4 to get -9.

$$3x-9-\frac{5}{3}\left(\frac{3}{2}x+1\right)$$

Use the distributive property to multiply -\frac{5}{3} by \frac{3}{2}x+1.

$$3x-9-\frac{5}{3}\times \frac{3}{2}x-\frac{5}{3}$$

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

$$3x-9+\frac{-5\times 3}{3\times 2}x-\frac{5}{3}$$

Cancel out 3 in both numerator and denominator.

$$3x-9+\frac{-5}{2}x-\frac{5}{3}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$3x-9-\frac{5}{2}x-\frac{5}{3}$$

Combine 3x and -\frac{5}{2}x to get \frac{1}{2}x.

$$\frac{1}{2}x-9-\frac{5}{3}$$

Convert -9 to fraction -\frac{27}{3}.

$$\frac{1}{2}x-\frac{27}{3}-\frac{5}{3}$$

Since -\frac{27}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x+\frac{-27-5}{3}$$

Subtract 5 from -27 to get -32.

$$\frac{1}{2}x-\frac{32}{3}$$