Solve 3(x-1)/2-4(2x+5)/5=2x+8x-1/2

$$\frac { 3 ( x - 1 ) } { 2 } - \frac { 4 ( 2 x + 5 ) } { 5 } = 2 x + \frac { 8 x - 1 } { 2 }$$

Solve for x

$$x=-\frac{50}{61}\approx -0.819672131$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 2,5.

$$5\times 3\left(x-1\right)-2\times 4\left(2x+5\right)=20x+5\left(8x-1\right)$$

Multiply 5 and 3 to get 15.

$$15\left(x-1\right)-2\times 4\left(2x+5\right)=20x+5\left(8x-1\right)$$

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

$$15x-15-2\times 4\left(2x+5\right)=20x+5\left(8x-1\right)$$

Multiply -2 and 4 to get -8.

$$15x-15-8\left(2x+5\right)=20x+5\left(8x-1\right)$$

Use the distributive property to multiply -8 by 2x+5.

$$15x-15-16x-40=20x+5\left(8x-1\right)$$

Combine 15x and -16x to get -x.

$$-x-15-40=20x+5\left(8x-1\right)$$

Subtract 40 from -15 to get -55.

$$-x-55=20x+5\left(8x-1\right)$$

Use the distributive property to multiply 5 by 8x-1.

$$-x-55=20x+40x-5$$

Combine 20x and 40x to get 60x.

$$-x-55=60x-5$$

Subtract 60x from both sides.

$$-x-55-60x=-5$$

Combine -x and -60x to get -61x.

$$-61x-55=-5$$

Add 55 to both sides.

$$-61x=-5+55$$

Add -5 and 55 to get 50.

$$-61x=50$$

Divide both sides by -61.

$$x=\frac{50}{-61}$$

Fraction \frac{50}{-61} can be rewritten as -\frac{50}{61} by extracting the negative sign.

$$x=-\frac{50}{61}$$