Question

Let x equal -3m -2n -4.What happens to the value of x if the value of m increases by 2 and the value of n decreases by 1?

Answer 1

The value of x decreases by 5

Step-by-step explanation:

The initial value of x is:

x = -3m - 2n - 4

If we increase m by 2 and decrease n by 1, we will need to change m by m+2 and n by n-1. So, we can calculate a new value for x, that I will call x₂ as:

`x_2=-3(m+2)-2(n-1)-4`

Now, we can solve for x₂ as:

`\begin{gathered} x_2=-(3\cdot m)-(3\cdot2)-(2\cdot n)-2(-1)-4 \\ x_2=-3m-6-2n+1-4 \\ x_2=-3m-2n-9 \end{gathered}`

Then, we can write -9 as -4 - 5 so:

`x_2=\textcolor{#FF7968}{-3m-2n-4}-5`

Since -3m-2n-4 is equal to x, x₂ is equal to:

`x_2=x-5`

Therefore, if the value of m increases by 2 and the value of n decreases by 1, then the value of x decreases by 5.