Solve 3(2x-1/3)+2(1/4x-5)=1/4-3x

$$3 ( 2 x - \frac { 1 } { 3 } ) + 2 ( \frac { 1 } { 4 } x - 5 ) = \frac { 1 } { 4 } - 3 x$$

Solve for x

$$x = \frac{45}{38} = 1\frac{7}{38} \approx 1.184210526$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 2x-\frac{1}{3}.

$$6x+3\left(-\frac{1}{3}\right)+2\left(\frac{1}{4}x-5\right)=\frac{1}{4}-3x$$

Cancel out 3 and 3.

$$6x-1+2\left(\frac{1}{4}x-5\right)=\frac{1}{4}-3x$$

Use the distributive property to multiply 2 by \frac{1}{4}x-5.

$$6x-1+2\times \frac{1}{4}x-10=\frac{1}{4}-3x$$

Multiply 2 and \frac{1}{4} to get \frac{2}{4}.

$$6x-1+\frac{2}{4}x-10=\frac{1}{4}-3x$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$6x-1+\frac{1}{2}x-10=\frac{1}{4}-3x$$

Combine 6x and \frac{1}{2}x to get \frac{13}{2}x.

$$\frac{13}{2}x-1-10=\frac{1}{4}-3x$$

Subtract 10 from -1 to get -11.

$$\frac{13}{2}x-11=\frac{1}{4}-3x$$

Add 3x to both sides.

$$\frac{13}{2}x-11+3x=\frac{1}{4}$$

Combine \frac{13}{2}x and 3x to get \frac{19}{2}x.

$$\frac{19}{2}x-11=\frac{1}{4}$$

Add 11 to both sides.

$$\frac{19}{2}x=\frac{1}{4}+11$$

Convert 11 to fraction \frac{44}{4}.

$$\frac{19}{2}x=\frac{1}{4}+\frac{44}{4}$$

Since \frac{1}{4} and \frac{44}{4} have the same denominator, add them by adding their numerators.

$$\frac{19}{2}x=\frac{1+44}{4}$$

Add 1 and 44 to get 45.

$$\frac{19}{2}x=\frac{45}{4}$$

Multiply both sides by \frac{2}{19}, the reciprocal of \frac{19}{2}.

$$x=\frac{45}{4}\times \frac{2}{19}$$

Multiply \frac{45}{4} times \frac{2}{19} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{45\times 2}{4\times 19}$$

Do the multiplications in the fraction \frac{45\times 2}{4\times 19}.

$$x=\frac{90}{76}$$

Reduce the fraction \frac{90}{76} to lowest terms by extracting and canceling out 2.

$$x=\frac{45}{38}$$