Question

Solve for x: 5 over 8 equals the quantity x minus 1 end quantity over 9

37 over 8
23 over 4
11 over 2
53 over 8

Answer 1

The solution to the equation is
`x=(53)/(8)`.

Explanation:

We have the equation
`(5)/(8) = (x-1)/(9)`. In order to solve it we can make cross multiplication:

`9\cdot 5 = 8(x-1)`

which is equivalent to

`45=8x-8`.

Now we isolate the unknown x in the right hand side of the equation:

`45+8=8x`.

Thus,
`53=8x`, Dividing both sides of the equation by 8 we get the final solution:

`x=(53)/(8)`.

We can check our solution substituting the value of x in the original equation:

`((53)/(8)-1)/(9) = ((53)/(8) - (8)/(8))/(9) = ((45)/(8))/(9) = (45)/(8\cdot 9) = (5)/(8)`.

Hence, we have the correct solution.

Answer 2

53/8

Explanation:

`(5)/(8)=(x-1)/(9)\\\\45=8x-8 \qquad\text{multiply by 72}\\\\53=8x \qquad\text{add 8}\\\\(53)/(8)=x \qquad\text{divide by 8}`