Solve -6/5+4/7x+62=17-x

$$- \frac { 6 } { 5 } + \frac { 4 } { 7 } x + 62 = 17 - x$$

Solve for x

$$x = -\frac{1533}{55} = -27\frac{48}{55} \approx -27.872727273$$

Steps for Solving Linear Equation

Convert 62 to fraction \frac{310}{5}.

$$-\frac{6}{5}+\frac{4}{7}x+\frac{310}{5}=17-x$$

Since -\frac{6}{5} and \frac{310}{5} have the same denominator, add them by adding their numerators.

$$\frac{-6+310}{5}+\frac{4}{7}x=17-x$$

Add -6 and 310 to get 304.

$$\frac{304}{5}+\frac{4}{7}x=17-x$$

Add x to both sides.

$$\frac{304}{5}+\frac{4}{7}x+x=17$$

Combine \frac{4}{7}x and x to get \frac{11}{7}x.

$$\frac{304}{5}+\frac{11}{7}x=17$$

Subtract \frac{304}{5} from both sides.

$$\frac{11}{7}x=17-\frac{304}{5}$$

Convert 17 to fraction \frac{85}{5}.

$$\frac{11}{7}x=\frac{85}{5}-\frac{304}{5}$$

Since \frac{85}{5} and \frac{304}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{7}x=\frac{85-304}{5}$$

Subtract 304 from 85 to get -219.

$$\frac{11}{7}x=-\frac{219}{5}$$

Multiply both sides by \frac{7}{11}, the reciprocal of \frac{11}{7}.

$$x=-\frac{219}{5}\times \frac{7}{11}$$

Multiply -\frac{219}{5} times \frac{7}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-219\times 7}{5\times 11}$$

Do the multiplications in the fraction \frac{-219\times 7}{5\times 11}.

$$x=\frac{-1533}{55}$$

Fraction \frac{-1533}{55} can be rewritten as -\frac{1533}{55} by extracting the negative sign.

$$x=-\frac{1533}{55}$$