Solve {l}{3/4(x-3)}{-4(x+5)}

$$\left. \begin{array} { l } { \frac { 3 } { 4 } ( x - 3 ) } \\ { - 4 ( x + 5 ) } \end{array} \right.$$

Evaluate

$$\frac{-13x-89}{4}$$

Solution Steps

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

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

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

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

Multiply 3 and -3 to get -9.

$$\frac{3}{4}x+\frac{-9}{4}-4\left(x+5\right)$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$\frac{3}{4}x-\frac{9}{4}-4\left(x+5\right)$$

Use the distributive property to multiply -4 by x+5.

$$\frac{3}{4}x-\frac{9}{4}-4x-20$$

Combine \frac{3}{4}x and -4x to get -\frac{13}{4}x.

$$-\frac{13}{4}x-\frac{9}{4}-20$$

Convert 20 to fraction \frac{80}{4}.

$$-\frac{13}{4}x-\frac{9}{4}-\frac{80}{4}$$

Since -\frac{9}{4} and \frac{80}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{4}x+\frac{-9-80}{4}$$

Subtract 80 from -9 to get -89.

$$-\frac{13}{4}x-\frac{89}{4}$$

Expand

$$\frac{-13x-89}{4}$$

Solution Steps

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

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

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

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

Multiply 3 and -3 to get -9.

$$\frac{3}{4}x+\frac{-9}{4}-4\left(x+5\right)$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$\frac{3}{4}x-\frac{9}{4}-4\left(x+5\right)$$

Use the distributive property to multiply -4 by x+5.

$$\frac{3}{4}x-\frac{9}{4}-4x-20$$

Combine \frac{3}{4}x and -4x to get -\frac{13}{4}x.

$$-\frac{13}{4}x-\frac{9}{4}-20$$

Convert 20 to fraction \frac{80}{4}.

$$-\frac{13}{4}x-\frac{9}{4}-\frac{80}{4}$$

Since -\frac{9}{4} and \frac{80}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{4}x+\frac{-9-80}{4}$$

Subtract 80 from -9 to get -89.

$$-\frac{13}{4}x-\frac{89}{4}$$