Solve -5x+3(-5/8x-11/4)=-22

$$- 5 x + 3 ( - 5 / 8 x - 11 / 4 ) = - 22$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by -\frac{5}{8}x-\frac{11}{4}.

$$-5x+3\left(-\frac{5}{8}\right)x+3\left(-\frac{11}{4}\right)=-22$$

Express 3\left(-\frac{5}{8}\right) as a single fraction.

$$-5x+\frac{3\left(-5\right)}{8}x+3\left(-\frac{11}{4}\right)=-22$$

Multiply 3 and -5 to get -15.

$$-5x+\frac{-15}{8}x+3\left(-\frac{11}{4}\right)=-22$$

Fraction \frac{-15}{8} can be rewritten as -\frac{15}{8} by extracting the negative sign.

$$-5x-\frac{15}{8}x+3\left(-\frac{11}{4}\right)=-22$$

Express 3\left(-\frac{11}{4}\right) as a single fraction.

$$-5x-\frac{15}{8}x+\frac{3\left(-11\right)}{4}=-22$$

Multiply 3 and -11 to get -33.

$$-5x-\frac{15}{8}x+\frac{-33}{4}=-22$$

Fraction \frac{-33}{4} can be rewritten as -\frac{33}{4} by extracting the negative sign.

$$-5x-\frac{15}{8}x-\frac{33}{4}=-22$$

Combine -5x and -\frac{15}{8}x to get -\frac{55}{8}x.

$$-\frac{55}{8}x-\frac{33}{4}=-22$$

Add \frac{33}{4} to both sides.

$$-\frac{55}{8}x=-22+\frac{33}{4}$$

Convert -22 to fraction -\frac{88}{4}.

$$-\frac{55}{8}x=-\frac{88}{4}+\frac{33}{4}$$

Since -\frac{88}{4} and \frac{33}{4} have the same denominator, add them by adding their numerators.

$$-\frac{55}{8}x=\frac{-88+33}{4}$$

Add -88 and 33 to get -55.

$$-\frac{55}{8}x=-\frac{55}{4}$$

Multiply both sides by -\frac{8}{55}, the reciprocal of -\frac{55}{8}.

$$x=-\frac{55}{4}\left(-\frac{8}{55}\right)$$

Multiply -\frac{55}{4} times -\frac{8}{55} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-55\left(-8\right)}{4\times 55}$$

Do the multiplications in the fraction \frac{-55\left(-8\right)}{4\times 55}.

$$x=\frac{440}{220}$$

Divide 440 by 220 to get 2.

$$x=2$$