Solve 3-5/4-3-6/7-x=5

$$3 \frac{ -5 }{ 4 } -3 \frac{ -6 }{ 7 } -x = 5$$

Solve for x

$$x = -\frac{173}{28} = -6\frac{5}{28} \approx -6.178571429$$

Steps for Solving Linear Equation

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$3\left(-\frac{5}{4}\right)-3\times \frac{-6}{7}-x=5$$

Express 3\left(-\frac{5}{4}\right) as a single fraction.

$$\frac{3\left(-5\right)}{4}-3\times \frac{-6}{7}-x=5$$

Multiply 3 and -5 to get -15.

$$\frac{-15}{4}-3\times \frac{-6}{7}-x=5$$

Fraction \frac{-15}{4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$-\frac{15}{4}-3\times \frac{-6}{7}-x=5$$

Fraction \frac{-6}{7} can be rewritten as -\frac{6}{7} by extracting the negative sign.

$$-\frac{15}{4}-3\left(-\frac{6}{7}\right)-x=5$$

Express 3\left(-\frac{6}{7}\right) as a single fraction.

$$-\frac{15}{4}-\frac{3\left(-6\right)}{7}-x=5$$

Multiply 3 and -6 to get -18.

$$-\frac{15}{4}-\frac{-18}{7}-x=5$$

Fraction \frac{-18}{7} can be rewritten as -\frac{18}{7} by extracting the negative sign.

$$-\frac{15}{4}-\left(-\frac{18}{7}\right)-x=5$$

The opposite of -\frac{18}{7} is \frac{18}{7}.

$$-\frac{15}{4}+\frac{18}{7}-x=5$$

Least common multiple of 4 and 7 is 28. Convert -\frac{15}{4} and \frac{18}{7} to fractions with denominator 28.

$$-\frac{105}{28}+\frac{72}{28}-x=5$$

Since -\frac{105}{28} and \frac{72}{28} have the same denominator, add them by adding their numerators.

$$\frac{-105+72}{28}-x=5$$

Add -105 and 72 to get -33.

$$-\frac{33}{28}-x=5$$

Add \frac{33}{28} to both sides.

$$-x=5+\frac{33}{28}$$

Convert 5 to fraction \frac{140}{28}.

$$-x=\frac{140}{28}+\frac{33}{28}$$

Since \frac{140}{28} and \frac{33}{28} have the same denominator, add them by adding their numerators.

$$-x=\frac{140+33}{28}$$

Add 140 and 33 to get 173.

$$-x=\frac{173}{28}$$

Multiply both sides by -1.

$$x=-\frac{173}{28}$$