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

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

Solve for x

$$x = -\frac{27}{4} = -6\frac{3}{4} = -6.75$$

Steps for Solving Linear Equation

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

$$-2\times 2\left(x+3\right)+3\times 5\left(2x-1\right)=30x$$

Multiply -2 and 2 to get -4.

$$-4\left(x+3\right)+3\times 5\left(2x-1\right)=30x$$

Use the distributive property to multiply -4 by x+3.

$$-4x-12+3\times 5\left(2x-1\right)=30x$$

Multiply 3 and 5 to get 15.

$$-4x-12+15\left(2x-1\right)=30x$$

Use the distributive property to multiply 15 by 2x-1.

$$-4x-12+30x-15=30x$$

Combine -4x and 30x to get 26x.

$$26x-12-15=30x$$

Subtract 15 from -12 to get -27.

$$26x-27=30x$$

Subtract 30x from both sides.

$$26x-27-30x=0$$

Combine 26x and -30x to get -4x.

$$-4x-27=0$$

Add 27 to both sides. Anything plus zero gives itself.

$$-4x=27$$

Divide both sides by -4.

$$x=\frac{27}{-4}$$

Fraction \frac{27}{-4} can be rewritten as -\frac{27}{4} by extracting the negative sign.

$$x=-\frac{27}{4}$$