After you move the $4$, you will have an inequality with $-2x$ on one side. What happens to the inequality sign when you divide both sides by a negative number?

Once you have an inequality like $x$ compared to a number, check each answer choice to see which one satisfies that comparison.

In Desmos, type 4 - 2x > 6. Desmos will shade the region of the number line (or graph) that represents all $x$ values satisfying this inequality.

Look at the shaded part and the open or closed circle on the boundary point to see what condition on $x$ the graph represents (for example, all $x$ less than some number).

Type each choice as a separate expression, such as x = -1, x = 0, x = 2, and x = -3, and see which vertical line lies completely within the shaded solution region of the inequality.

Start with the given inequality:

Subtract $4$ from both sides to begin isolating $x$:

Now divide both sides by $-2$ to solve for $x$. When you divide or multiply an inequality by a negative number, you must reverse the inequality sign:

So the solution set is all real numbers $x$ such that $x$ is less than $-1$. It’s not just one number; it’s every number smaller than $-1$.

Now compare each answer choice to the condition $x < -1$:

• $-1$ is not less than $-1$ (it is equal), so it does not work.
• $0$ is greater than $-1$, so it does not work.
• $2$ is greater than $-1$, so it does not work.
• $-3$ is less than $-1$, so it does work.

Therefore, the value of $x$ that is a solution to the inequality is $-3$.