Solve 1/3(5x+6)-1/2(x+7)=2

$$\frac { 1 } { 3 } ( 5 x + 6 ) - \frac { 1 } { 2 } ( x + 7 ) = 2$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 5x+6.

$$\frac{1}{3}\times 5x+\frac{1}{3}\times 6-\frac{1}{2}\left(x+7\right)=2$$

Multiply \frac{1}{3} and 5 to get \frac{5}{3}.

$$\frac{5}{3}x+\frac{1}{3}\times 6-\frac{1}{2}\left(x+7\right)=2$$

Multiply \frac{1}{3} and 6 to get \frac{6}{3}.

$$\frac{5}{3}x+\frac{6}{3}-\frac{1}{2}\left(x+7\right)=2$$

Divide 6 by 3 to get 2.

$$\frac{5}{3}x+2-\frac{1}{2}\left(x+7\right)=2$$

Use the distributive property to multiply -\frac{1}{2} by x+7.

$$\frac{5}{3}x+2-\frac{1}{2}x-\frac{1}{2}\times 7=2$$

Express -\frac{1}{2}\times 7 as a single fraction.

$$\frac{5}{3}x+2-\frac{1}{2}x+\frac{-7}{2}=2$$

Fraction \frac{-7}{2} can be rewritten as -\frac{7}{2} by extracting the negative sign.

$$\frac{5}{3}x+2-\frac{1}{2}x-\frac{7}{2}=2$$

Combine \frac{5}{3}x and -\frac{1}{2}x to get \frac{7}{6}x.

$$\frac{7}{6}x+2-\frac{7}{2}=2$$

Convert 2 to fraction \frac{4}{2}.

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

Since \frac{4}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 7 from 4 to get -3.

$$\frac{7}{6}x-\frac{3}{2}=2$$

Add \frac{3}{2} to both sides.

$$\frac{7}{6}x=2+\frac{3}{2}$$

Convert 2 to fraction \frac{4}{2}.

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

Since \frac{4}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

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

Add 4 and 3 to get 7.

$$\frac{7}{6}x=\frac{7}{2}$$

Multiply both sides by \frac{6}{7}, the reciprocal of \frac{7}{6}.

$$x=\frac{7}{2}\times \frac{6}{7}$$

Multiply \frac{7}{2} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\times 6}{2\times 7}$$

Cancel out 7 in both numerator and denominator.

$$x=\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$x=3$$