Question

pasha is thinking of a number such that when twice the number is added to three times one more than the number she gets the same result as when she multiplies four times one less than the number. what number is pasha thinking about?

Answer 1

This is the equation made from the problem where x=mystery number
2x+3(x+1)=4(x-1)

Now let's solve for x!

We start by distributing 3 into (X+1)

3(x)=3x and 3(1)=3

Now our equation is 2x+3x+3=4(x-1)

Let's combine both x values on the left side of the equation: 2x + 3x=5x

We now have 5x+3=4(x-1)

Let's distribute 4 into (x-1)

4(x)=4x and 4(-1)=-4

Now our equation is 5x+3=4x-4

subtract 3 form both sides

5x=4x-7

subtract 4x from both sides

x=-7

Yay! So the number she is thinking of is -7!

Answer 2

The number is -7.

Explanation:

Let the number be = x

when twice the number is added to three times one more than the number. Mathematically, we can denote this as:

`2x+3(x+1)`

She gets the same result as when she multiplies four times one less than the number.

`4(x-1)`

Now, both the results are same, so we will equate them same.

`2x+3(x+1)=4(x-1)`

=>
`2x+3x+3=4x-4`

=>
`5x+3=4x-4`

=>
`5x-4x=-4-3`

This gives x = -7

So, the number Pasha was thinking was -7.

We can check this:

`2(-7)+3(-7+1)=4(-7-1)`

=>
`-14+3(-6)=4(-8)`

=>
`-14-18=-32`

=>
`-32=-32` (checked)