Solve 3/7(x+3)+5=3x+2?

$$\frac { 3 } { 7 } ( x + 3 ) + 5 = 3 x + 2 ?$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{7} by x+3.

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

Express \frac{3}{7}\times 3 as a single fraction.

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

Multiply 3 and 3 to get 9.

$$\frac{3}{7}x+\frac{9}{7}+5=3x+2$$

Convert 5 to fraction \frac{35}{7}.

$$\frac{3}{7}x+\frac{9}{7}+\frac{35}{7}=3x+2$$

Since \frac{9}{7} and \frac{35}{7} have the same denominator, add them by adding their numerators.

$$\frac{3}{7}x+\frac{9+35}{7}=3x+2$$

Add 9 and 35 to get 44.

$$\frac{3}{7}x+\frac{44}{7}=3x+2$$

Subtract 3x from both sides.

$$\frac{3}{7}x+\frac{44}{7}-3x=2$$

Combine \frac{3}{7}x and -3x to get -\frac{18}{7}x.

$$-\frac{18}{7}x+\frac{44}{7}=2$$

Subtract \frac{44}{7} from both sides.

$$-\frac{18}{7}x=2-\frac{44}{7}$$

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

$$-\frac{18}{7}x=\frac{14}{7}-\frac{44}{7}$$

Since \frac{14}{7} and \frac{44}{7} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{18}{7}x=\frac{14-44}{7}$$

Subtract 44 from 14 to get -30.

$$-\frac{18}{7}x=-\frac{30}{7}$$

Multiply both sides by -\frac{7}{18}, the reciprocal of -\frac{18}{7}.

$$x=-\frac{30}{7}\left(-\frac{7}{18}\right)$$

Multiply -\frac{30}{7} times -\frac{7}{18} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-30\left(-7\right)}{7\times 18}$$

Do the multiplications in the fraction \frac{-30\left(-7\right)}{7\times 18}.

$$x=\frac{210}{126}$$

Reduce the fraction \frac{210}{126} to lowest terms by extracting and canceling out 42.

$$x=\frac{5}{3}$$