Solve x-5/5-7-2x/2=3(2x+5)-1

$$\frac { x - 5 } { 5 } - \frac { 7 - 2 x } { 2 } = 3 ( 2 x + 5 ) - 1$$

Solve for x

$$x = -\frac{185}{48} = -3\frac{41}{48} \approx -3.854166667$$

Steps for Solving Linear Equation

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

$$2\left(x-5\right)-5\left(7-2x\right)=30\left(2x+5\right)-10$$

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

$$2x-10-5\left(7-2x\right)=30\left(2x+5\right)-10$$

Use the distributive property to multiply -5 by 7-2x.

$$2x-10-35+10x=30\left(2x+5\right)-10$$

Subtract 35 from -10 to get -45.

$$2x-45+10x=30\left(2x+5\right)-10$$

Combine 2x and 10x to get 12x.

$$12x-45=30\left(2x+5\right)-10$$

Use the distributive property to multiply 30 by 2x+5.

$$12x-45=60x+150-10$$

Subtract 10 from 150 to get 140.

$$12x-45=60x+140$$

Subtract 60x from both sides.

$$12x-45-60x=140$$

Combine 12x and -60x to get -48x.

$$-48x-45=140$$

Add 45 to both sides.

$$-48x=140+45$$

Add 140 and 45 to get 185.

$$-48x=185$$

Divide both sides by -48.

$$x=\frac{185}{-48}$$

Fraction \frac{185}{-48} can be rewritten as -\frac{185}{48} by extracting the negative sign.

$$x=-\frac{185}{48}$$