Try moving the whole-number terms (like $-3$ and $4$) to one side of the equation and the fraction terms involving $\frac{1}{y+2}$ to the other side.

Once you have a single fraction like $\frac{\text{(number)}}{y+2}$ equal to a constant, multiply both sides by $y+2$ to eliminate the denominator and get a simple linear equation in $y$.

After you solve for $y$ exactly, turn the fraction into a decimal (or compare it to nearby integers) to decide which of the given intervals it falls between.

In the first line, type f(x) = 6/(x+2) - 3. In the second line, type g(x) = 4 - 2/(x+2). Here, let $x$ stand for $y$ from the problem.

Look for the point where the graphs of $f(x)$ and $g(x)$ intersect. Tap or click on that intersection to see its $x$-coordinate, which is the solution of the equation.

Compare the $x$-value you see at the intersection with the integers $-1$, $0$, and $1$. Decide between which two consecutive integers it lies, then choose the answer option whose interval matches that placement.

The equation is

Notice that the variable $y$ appears inside the same denominator $y+2$ on both sides. Also, $y$ cannot be $-2$ because that would make the denominator $0$, which is not allowed.

Move the constant terms to one side and keep the fraction terms on the other side.

1. Add $3$ to both sides:

2. Add $\frac{2}{y+2}$ to both sides to put all fractions together:

3. Since the denominators are the same, combine the numerators:

To remove the fraction, multiply both sides of

by $y+2$ (remember $y\neq -2$):

Now you have a standard linear equation in $y$ with no fractions.

Solve

step by step:

Now approximate $-\frac{6}{7} \approx -0.86$. This number is greater than $-1$ and less than $0$, so $y$ lies between $-1$ and $0$, which matches choice C) -1 and 0.