Question

I JUST NEED HELP ON NOOOOOW

Answer 1

The solution to the equation is:

`x=-5`

Explanation:

Step 1: Rearrange the equation

Since we have to solve the equation for
`x`, let's bring the
`(x)/(6)` to the other side with all the other variables:

`(5x)/(3)-x=(x)/(6)-(5)/(2)\\\\\text{Subtract}~(x)/(6)~\text{from both sides of the equation:}\\(5x)/(3)-x-(x)/(6)=(x)/(6)-(x)/(6)-(5)/(2)\\\\\text{Simplify:}\\(5x)/(3)-x-(x)/(6)=-(5)/(2)`

Step 2: Make use of the distributive property

The property states that when there's an expression like
`3(2x+6)`, it can be written as
`3(2x)+3(6)`, or vice versa.

In the equation we have found above, the left hand side of the equation has a common variable:
`x`

Using the principle of distributive property, we can arrange the left hand side differently:

`(5x)/(3)-x-(x)/(6)=-(5)/(2)\\x((5)/(3)-1-(1)/(6))=-(5)/(2)`

We have arranged the left hand side as such, that distributive property is applicable for it.

Step 3: Solving

First, let's simplify the equation:

`x((5)/(3)-1-(1)/(6))=-(5)/(2)\\\\\text{Add the numbers inside the bracket:}\\x((1)/(2))=-(5)/(2)`

Now, let's solve it:

`(1)/(2)x=-(5)/(2)\\\\\text{Multiply both sides of the equation by}~2:\\(1)/(2)x* 2=-(5)/(2)* 2\\\\\text{Calculate:}\\(2)/(2)x=-(10)/(2)\\x=-5`