Solve 3x+5/2-[3x-5/12-(3x+17/6-7/3)]+frac{43}{12}=0

$$\frac { 3 x + 5 } { 2 } - [ \frac { 3 x - 5 } { 12 } - ( \frac { 3 x + 17 } { 6 } - \frac { 7 } { 3 } ) ] + \frac { 43 } { 12 } = 0$$

Solve for x

$$x=-4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,12,6,3.

$$12\left(\frac{3x+5}{2}-\left(\frac{3x-5}{12}-\left(\frac{3x+17}{6}-\frac{7}{3}\right)\right)\right)+43=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 3 is 6. Multiply \frac{7}{3} times \frac{2}{2}.

$$12\left(\frac{3x+5}{2}-\left(\frac{3x-5}{12}-\left(\frac{3x+17}{6}-\frac{7\times 2}{6}\right)\right)\right)+43=0$$

Since \frac{3x+17}{6} and \frac{7\times 2}{6} have the same denominator, subtract them by subtracting their numerators.

$$12\left(\frac{3x+5}{2}-\left(\frac{3x-5}{12}-\frac{3x+17-7\times 2}{6}\right)\right)+43=0$$

Do the multiplications in 3x+17-7\times 2.

$$12\left(\frac{3x+5}{2}-\left(\frac{3x-5}{12}-\frac{3x+17-14}{6}\right)\right)+43=0$$

Combine like terms in 3x+17-14.

$$12\left(\frac{3x+5}{2}-\left(\frac{3x-5}{12}-\frac{3x+3}{6}\right)\right)+43=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 6 is 12. Multiply \frac{3x+3}{6} times \frac{2}{2}.

$$12\left(\frac{3x+5}{2}-\left(\frac{3x-5}{12}-\frac{2\left(3x+3\right)}{12}\right)\right)+43=0$$

Since \frac{3x-5}{12} and \frac{2\left(3x+3\right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$12\left(\frac{3x+5}{2}-\frac{3x-5-2\left(3x+3\right)}{12}\right)+43=0$$

Do the multiplications in 3x-5-2\left(3x+3\right).

$$12\left(\frac{3x+5}{2}-\frac{3x-5-6x-6}{12}\right)+43=0$$

Combine like terms in 3x-5-6x-6.

$$12\left(\frac{3x+5}{2}-\frac{-3x-11}{12}\right)+43=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 12 is 12. Multiply \frac{3x+5}{2} times \frac{6}{6}.

$$12\left(\frac{6\left(3x+5\right)}{12}-\frac{-3x-11}{12}\right)+43=0$$

Since \frac{6\left(3x+5\right)}{12} and \frac{-3x-11}{12} have the same denominator, subtract them by subtracting their numerators.

$$12\times \frac{6\left(3x+5\right)-\left(-3x-11\right)}{12}+43=0$$

Do the multiplications in 6\left(3x+5\right)-\left(-3x-11\right).

$$12\times \frac{18x+30+3x+11}{12}+43=0$$

Combine like terms in 18x+30+3x+11.

$$12\times \frac{21x+41}{12}+43=0$$

Express 12\times \frac{21x+41}{12} as a single fraction.

$$\frac{12\left(21x+41\right)}{12}+43=0$$

Cancel out 12 and 12.

$$21x+41+43=0$$

Add 41 and 43 to get 84.

$$21x+84=0$$

Subtract 84 from both sides. Anything subtracted from zero gives its negation.

$$21x=-84$$

Divide both sides by 21.

$$x=\frac{-84}{21}$$

Divide -84 by 21 to get -4.

$$x=-4$$