Question

Rewrite the equation to a simpler equivalent form, then solve for x.


`(2x)/(5) +(9)/(10) =(7)/(10)`

Answer 1

Answer: The simpler equivalent form 4x + 9 =7.

Final answer
`x = -(1)/(2)`.

Step-by-step explanation: Given equation

`(2x)/(5) +(9)/(10) =(7)/(10)`.

First we need to write it in simpler form and then solve for x.

In order to write it in simpler equivalent form, we need to find the common denominator/ least common denominator.

We have 5, 10 and 10 in denominators.

LCM of 5 and 10 is 10.

Therefore, we need to multiply each term by 10 on the top and simplify to remove denominators.

Therefore,

`10*(2x)/(5) +10*(9)/(10) =10*(7)/(10)`

On simplifying this step, we get

2 × 2x + 9 = 7

4x + 9 =7.

This the simpler equivalent form.

Now, subtracting 9 from both sides, we get

4x+9-9 = 7-9

4x = -2

Dividing both sides by 4, we get

`(4x)/(4) =(-2)/(4)`

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