Solve 4x+5/6x=-9+1/4

$$4x+ \frac{ 5 }{ 6 } x=-9+ \frac{ 1 }{ 4 }$$

Solve for x

$$x = -\frac{105}{58} = -1\frac{47}{58} \approx -1.810344828$$

Steps for Solving Linear Equation

Combine 4x and \frac{5}{6}x to get \frac{29}{6}x.

$$\frac{29}{6}x=-9+\frac{1}{4}$$

Convert -9 to fraction -\frac{36}{4}.

$$\frac{29}{6}x=-\frac{36}{4}+\frac{1}{4}$$

Since -\frac{36}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{29}{6}x=\frac{-36+1}{4}$$

Add -36 and 1 to get -35.

$$\frac{29}{6}x=-\frac{35}{4}$$

Multiply both sides by \frac{6}{29}, the reciprocal of \frac{29}{6}.

$$x=-\frac{35}{4}\times \frac{6}{29}$$

Multiply -\frac{35}{4} times \frac{6}{29} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-35\times 6}{4\times 29}$$

Do the multiplications in the fraction \frac{-35\times 6}{4\times 29}.

$$x=\frac{-210}{116}$$

Reduce the fraction \frac{-210}{116} to lowest terms by extracting and canceling out 2.

$$x=-\frac{105}{58}$$