Try to isolate $x$ step by step. What operation will remove the $+6$ from the middle expression $2x + 6$? Make sure you apply that operation to all three parts of the inequality.

After you remove the $+6$, you will have something like a number $<$ or $\le$ $2x$ $<$ or $\le$ another number. What should you divide by to get $x$ alone, and do you need to flip the inequality signs?

Once you have an interval for $x$ (like $a < x \le b$), check each answer choice against that interval. Pay close attention to which endpoint is strict ($<$) and which is inclusive ($\le$).

In Desmos, enter the equation y = 2x + 6. This shows the line representing $2x + 6$ for all $x$.

Enter y = -4 and y = 10 as two more equations. These horizontal lines represent the lower and upper bounds for $2x + 6$ in the inequality $-4 < 2x + 6 \le 10$.

Click on the y = 2x + 6 equation and add a table. In the $x$-column, type the four answer choices: $-6$, $-1$, $4$, and $7$. Look at the corresponding $y$-values in the table and check which row has a $y$-value that is greater than $-4$ and less than or equal to $10$. The $x$ in that row is the value that satisfies the compound inequality.

The inequality

is a compound inequality, meaning $2x + 6$ must be greater than $-4$ and less than or equal to $10$ at the same time. We will solve it as a three-part inequality to find all possible $x$ values.

To isolate $x$, first get rid of the $+6$ by subtracting $6$ from every part of the inequality:

which simplifies to

The inequality signs stay the same because we are just subtracting a number.

Now divide every part by $2$ to solve for $x$:

which simplifies to

We do not flip the inequality signs because we are dividing by a positive number.

The solution set is all real numbers $x$ such that

Now check each answer choice:

• $-6$ is not greater than $-5$.
• $4$ and $7$ are greater than $2$.
• $-1$ is greater than $-5$ and less than or equal to $2$.

So the only value that satisfies the compound inequality is $-1$ (choice B).