Solve 5/3+1/2=3div18*(x-1)

$$\frac{ 5 }{ 3 } + \frac{ 1 }{ 2 } =3 \div 18 \times (x-1)$$

Solve for x

$$x=14$$

Steps for Solving Linear Equation

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{10}{6}+\frac{3}{6}=\frac{3}{18}\left(x-1\right)$$

Since \frac{10}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{10+3}{6}=\frac{3}{18}\left(x-1\right)$$

Add 10 and 3 to get 13.

$$\frac{13}{6}=\frac{3}{18}\left(x-1\right)$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{13}{6}=\frac{1}{6}\left(x-1\right)$$

Use the distributive property to multiply \frac{1}{6} by x-1.

$$\frac{13}{6}=\frac{1}{6}x+\frac{1}{6}\left(-1\right)$$

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

$$\frac{13}{6}=\frac{1}{6}x-\frac{1}{6}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{6}x-\frac{1}{6}=\frac{13}{6}$$

Add \frac{1}{6} to both sides.

$$\frac{1}{6}x=\frac{13}{6}+\frac{1}{6}$$

Since \frac{13}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}x=\frac{13+1}{6}$$

Add 13 and 1 to get 14.

$$\frac{1}{6}x=\frac{14}{6}$$

Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}x=\frac{7}{3}$$

Multiply both sides by 6, the reciprocal of \frac{1}{6}.

$$x=\frac{7}{3}\times 6$$

Express \frac{7}{3}\times 6 as a single fraction.

$$x=\frac{7\times 6}{3}$$

Multiply 7 and 6 to get 42.

$$x=\frac{42}{3}$$

Divide 42 by 3 to get 14.

$$x=14$$