Solve 2(2x-1)/3+3(2x-1)/4-5*2x-1/6=0

$$\frac { 2 ( 2 x - 1 ) } { 3 } + \frac { 3 ( 2 x - 1 ) } { 4 } - 5 \cdot \frac { 2 x - 1 } { 6 } = 0$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,6.

$$12\left(\frac{2\left(2x-1\right)}{3}+\frac{3\left(2x-1\right)}{4}\right)-10\left(2x-1\right)=0$$

Use the distributive property to multiply 2 by 2x-1.

$$12\left(\frac{4x-2}{3}+\frac{3\left(2x-1\right)}{4}\right)-10\left(2x-1\right)=0$$

Use the distributive property to multiply 3 by 2x-1.

$$12\left(\frac{4x-2}{3}+\frac{6x-3}{4}\right)-10\left(2x-1\right)=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 4 is 12. Multiply \frac{4x-2}{3} times \frac{4}{4}. Multiply \frac{6x-3}{4} times \frac{3}{3}.

$$12\left(\frac{4\left(4x-2\right)}{12}+\frac{3\left(6x-3\right)}{12}\right)-10\left(2x-1\right)=0$$

Since \frac{4\left(4x-2\right)}{12} and \frac{3\left(6x-3\right)}{12} have the same denominator, add them by adding their numerators.

$$12\times \frac{4\left(4x-2\right)+3\left(6x-3\right)}{12}-10\left(2x-1\right)=0$$

Do the multiplications in 4\left(4x-2\right)+3\left(6x-3\right).

$$12\times \frac{16x-8+18x-9}{12}-10\left(2x-1\right)=0$$

Combine like terms in 16x-8+18x-9.

$$12\times \frac{34x-17}{12}-10\left(2x-1\right)=0$$

Express 12\times \frac{34x-17}{12} as a single fraction.

$$\frac{12\left(34x-17\right)}{12}-10\left(2x-1\right)=0$$

Cancel out 12 and 12.

$$34x-17-10\left(2x-1\right)=0$$

Use the distributive property to multiply -10 by 2x-1.

$$34x-17-20x+10=0$$

Combine 34x and -20x to get 14x.

$$14x-17+10=0$$

Add -17 and 10 to get -7.

$$14x-7=0$$

Add 7 to both sides. Anything plus zero gives itself.

$$14x=7$$

Divide both sides by 14.

$$x=\frac{7}{14}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$x=\frac{1}{2}$$