Question

how do i solve the following :
x-10/5 + 2/5 = -x/3

Answer 1

x-(10)/(5)+(2)/(5)=-(x)/(3)

Multiply each term in the equation by 3.
x*3-(10)/(5)*3+(2)/(5)*3=-(x)/(3)*3

Simplify the left-hand side of the equation by canceling the common factors.
3x-6+(6)/(5)=-(x)/(3)*3

Simplify the right-hand side of the equation by simplifying each term.
3x-6+(6)/(5)=-x

Since -x contains the variable to solve for, move it to the left-hand side of the equation by adding x to both sides.
3x-6+(6)/(5)+x=0

Since 3x and x are like terms, add x to 3x to get 4x.
4x-6+(6)/(5)=0

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 5. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
4x-6*(5)/(5)+(6)/(5)=0

Complete the multiplication to produce a denominator of 5 in each expression.
4x-(30)/(5)+(6)/(5)=0

Combine the numerators of all fractions that have common denominators.
4x+(-30+6)/(5)=0

Add 6 to -30 to get -24.
4x+(-24)/(5)=0

Move the minus sign from the numerator to the front of the expression.
4x-(24)/(5)=0

Since -(24)/(5) does not contain the variable to solve for, move it to the right-hand side of the equation by adding (24)/(5) to both sides.
4x=(24)/(5)

Divide each term in the equation by 4.
(4x)/(4)=(24)/(5)*(1)/(4)

Simplify the left-hand side of the equation by canceling the common factors.
x=(24)/(5)*(1)/(4)

Simplify the right-hand side of the equation by simplifying each term.
x=(6)/(5)