Solve 5x-3/2-1=3x+1/5-x-1/10

$$\frac{ 5x-3 }{ 2 } -1 = \frac{ 3x+1 }{ 5 } - \frac{ x-1 }{ 10 }$$

Solve for x

$$x = \frac{7}{5} = 1\frac{2}{5} = 1.4$$

Steps for Solving Linear Equation

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

$$5\left(5x-3\right)-10=2\left(3x+1\right)-\left(x-1\right)$$

Use the distributive property to multiply 5 by 5x-3.

$$25x-15-10=2\left(3x+1\right)-\left(x-1\right)$$

Subtract 10 from -15 to get -25.

$$25x-25=2\left(3x+1\right)-\left(x-1\right)$$

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

$$25x-25=6x+2-\left(x-1\right)$$

To find the opposite of x-1, find the opposite of each term.

$$25x-25=6x+2-x-\left(-1\right)$$

The opposite of -1 is 1.

$$25x-25=6x+2-x+1$$

Combine 6x and -x to get 5x.

$$25x-25=5x+2+1$$

Add 2 and 1 to get 3.

$$25x-25=5x+3$$

Subtract 5x from both sides.

$$25x-25-5x=3$$

Combine 25x and -5x to get 20x.

$$20x-25=3$$

Add 25 to both sides.

$$20x=3+25$$

Add 3 and 25 to get 28.

$$20x=28$$

Divide both sides by 20.

$$x=\frac{28}{20}$$

Reduce the fraction \frac{28}{20} to lowest terms by extracting and canceling out 4.

$$x=\frac{7}{5}$$