Solve 3x+14-4/7(6x+4)=2-x

$$3 x + 14 - \frac { 4 } { 7 } ( 6 x + 4 ) = 2 - x$$

Solve for x

$$x=-17$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{4}{7} by 6x+4.

$$3x+14-\frac{4}{7}\times 6x-\frac{4}{7}\times 4=2-x$$

Express -\frac{4}{7}\times 6 as a single fraction.

$$3x+14+\frac{-4\times 6}{7}x-\frac{4}{7}\times 4=2-x$$

Multiply -4 and 6 to get -24.

$$3x+14+\frac{-24}{7}x-\frac{4}{7}\times 4=2-x$$

Fraction \frac{-24}{7} can be rewritten as -\frac{24}{7} by extracting the negative sign.

$$3x+14-\frac{24}{7}x-\frac{4}{7}\times 4=2-x$$

Express -\frac{4}{7}\times 4 as a single fraction.

$$3x+14-\frac{24}{7}x+\frac{-4\times 4}{7}=2-x$$

Multiply -4 and 4 to get -16.

$$3x+14-\frac{24}{7}x+\frac{-16}{7}=2-x$$

Fraction \frac{-16}{7} can be rewritten as -\frac{16}{7} by extracting the negative sign.

$$3x+14-\frac{24}{7}x-\frac{16}{7}=2-x$$

Combine 3x and -\frac{24}{7}x to get -\frac{3}{7}x.

$$-\frac{3}{7}x+14-\frac{16}{7}=2-x$$

Convert 14 to fraction \frac{98}{7}.

$$-\frac{3}{7}x+\frac{98}{7}-\frac{16}{7}=2-x$$

Since \frac{98}{7} and \frac{16}{7} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{7}x+\frac{98-16}{7}=2-x$$

Subtract 16 from 98 to get 82.

$$-\frac{3}{7}x+\frac{82}{7}=2-x$$

Add x to both sides.

$$-\frac{3}{7}x+\frac{82}{7}+x=2$$

Combine -\frac{3}{7}x and x to get \frac{4}{7}x.

$$\frac{4}{7}x+\frac{82}{7}=2$$

Subtract \frac{82}{7} from both sides.

$$\frac{4}{7}x=2-\frac{82}{7}$$

Convert 2 to fraction \frac{14}{7}.

$$\frac{4}{7}x=\frac{14}{7}-\frac{82}{7}$$

Since \frac{14}{7} and \frac{82}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{7}x=\frac{14-82}{7}$$

Subtract 82 from 14 to get -68.

$$\frac{4}{7}x=-\frac{68}{7}$$

Multiply both sides by \frac{7}{4}, the reciprocal of \frac{4}{7}.

$$x=-\frac{68}{7}\times \frac{7}{4}$$

Multiply -\frac{68}{7} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-68\times 7}{7\times 4}$$

Cancel out 7 in both numerator and denominator.

$$x=\frac{-68}{4}$$

Divide -68 by 4 to get -17.

$$x=-17$$