Question

Multi-Step Equation!!

Can someone please explain how to get this step by step?

Answer 1

`\boxed{\mbox \large a = (9)/(10) = 0.9}`

Explanation:

Equation to be solved is

`(5)/(3)a + (4)/(5) = a + (7)/(5)`

Step 1

Get rid of those annoying denominators by multiplying throughout 15. We choose 15 because it is the lowest common multiple of 3 and 5. Since 3 and are prime numbers the LCM is 3 x 5 = 15

`15 \cdot (5)/(3)a +15 \cdot (4)/(5) = 15\cdot a + 15\cdot (7)/(5)}`
==>
`25a + 12 = 15a + 21}\\`

Step 2

Subtract 15 from both sides:

==>
`25a -15a + 12 = 15a -15a + 21}\\\\\\ 10a + 12 = 21}\\`

Step 3

Subtract 21 from both sides

`10a + 12 -12 = 21 - 12\\\\`

`10a = 9`

Step 4

Divide by 10 both sides

`(10a)/(10) = (9)/(10)\\\\\implies a = (9)/(10) = 0.9`