Question

How to solve 3x - 1/2 = 8 1/2 please no links and do it step by step

Answer 1

`x=(3)/(2)`

Explanation:

Step 1. Put each term in
`3x-(1)/(2)` over the common denominator 2.

`(6x)/(2)-(1)/(2)`

Therefore we have
`((6x)/(2)-(1)/(2))=4`

Step 2.

Combine
`(6x)/(2)-(1)/(2)` into a single fraction.

`(6x-1)/(2)`

Therefore we have
`((1)/(2)(6x-1))=4` or
`(6x-1)/(2)=4`

Step 3.

Multiply both sides by a constant to simplify the equation.

Multiply both sides of
`(6x-1)/(2)=4` by 2:

`(2*(6x-1))/(2)=4*2`

Step 4.

Cancel the common terms in the numerator and denominator of
`(2*(6x-1))/(2)`

Then we get
`(2)/(2)*(6x-1)` which simplifies to
`(6x-1)`

So all together we have
`(6x-1)=2*4`

Step 5.

Multiply 2 and 4 together and remove the parenthesis.

`6x-1=8`

Step 6.

Isolate terms with the variable x to the left hand side.

So add 1 to both sides:

`6x+(1-1)=8+1`

Evaluate
`1-1=0` which cancels out

Step 7.

Add the like terms on the right side:

`6x=9`

Step 8.

Divide both sides by a constant to simplify the equation.

Divide both sides of
`6x=9` by 6.

`(6x)/(6) =(9)/(6)`

Any non-zero number divided by itself is 1.

`x=(9)/(6)` which simplifies to
`x=(3)/(2)`