Question

rewrite the expression as a sum.
6x - 8 - 4x + 2 = 6x + (-8) + (4x) + 2
subtracting a number is the same as adding the opposite of that number.
the expression has both addition and subtraction. writing an equivalent expression that only has addition can be a helpful way to start.
write an expression that is equivalent to 6x - 8 - 4x + 2.

Explanation:

Step1: Recall the rule of subtraction as adding opposite

Subtracting a number is the same as adding its opposite. So, $-4x$ can be written as $+(-4x)$. But in the given expression rewrite, we have $-4x$ as $+(4x)$? Wait, no, let's check the original expression: $6x - 8 - 4x + 2$. We know that $a - b = a + (-b)$, so $-4x$ is $+(-4x)$, but in the box, we need to find the coefficient. Wait, the original term is $-4x$, so when we rewrite subtraction as addition, $-4x = +(-4x)$, but in the given form $6x + (-8) + (\square x) + 2$. So the term $-4x$ should be written as $+(-4x)$, so the coefficient of $x$ is $-4$? Wait, no, the box is in front of $x$, so let's see: the original expression is $6x - 8 - 4x + 2$. Let's rewrite each subtraction as addition of opposite: $6x + (-8) + (-4x) + 2$. Wait, but the given form is $6x + (-8) + (4x)$? No, that can't be. Wait, maybe a typo? Wait, no, the problem says "Rewrite the expression as a sum" and the original expression is $6x - 8 - 4x + 2$. So let's break down each term:

• $6x$ remains as $6x$
• $-8$ is $+(-8)$
• $-4x$ is $+(-4x)$
• $+2$ remains as $+2$

But in the given box, it's written as $4x$? Wait, no, maybe I misread. Wait, the original expression is $6x - 8 - 4x + 2$, and the rewritten form is $6x + (-8) + (4x) + 2$? No, that would be wrong. Wait, maybe the sign is wrong. Wait, subtracting $4x$ is adding $-4x$, so the coefficient of $x$ in that term is $-4$. Wait, but the box is around $4$, maybe it's a negative? Wait, no, let's do the algebra. Let's look at the original expression: $6x - 8 - 4x + 2$. Let's combine like terms first to check. $6x - 4x = 2x$, and $-8 + 2 = -6$, so the expression simplifies to $2x - 6$. But the problem is about rewriting the subtraction as addition. So $-4x$ is $+(-4x)$, so the coefficient of $x$ in that term is $-4$. Wait, but the box is showing $4$, maybe it's a typo and should be $-4$? Wait, no, let's re-express the original expression step by step.

Original expression: $6x - 8 - 4x + 2$

Using the rule: $a - b = a + (-b)$, so:

• $6x$ is $6x$
• $-8$ is $+(-8)$
• $-4x$ is $+(-4x)$
• $+2$ is $+2$

So rewriting as a sum: $6x + (-8) + (-4x) + 2$. Therefore, the term with $x$ after $-8$ is $-4x$, so the coefficient in the box (which is the coefficient of $x$) should be $-4$. Wait, but the box is written as $4$, maybe the problem has a sign error? Wait, no, maybe I misread the original expression. Let me check again. The original expression is $6x - 8 - 4x + 2$, and the rewritten form is $6x + (-8) + (4x) + 2$? That would be incorrect. Wait, maybe the original expression was $6x - 8 + 4x + 2$? No, the user's image shows $6x - 8 - 4x + 2$. Wait, perhaps the box is supposed to have $-4$? Let's confirm with the rule: subtracting a number is adding its opposite. So $-4x = +(-4x)$, so the coefficient is $-4$.

Wait, maybe the problem is written with a mistake, but according to the rule, subtracting $4x$ is adding $-4x$, so the coefficient is $-4$. But the box is showing $4$, maybe it's a typo and the correct coefficient is $-4$. Wait, but let's check the original expression again. The user's image: "6x - 8 - 4x + 2 = 6x + (-8) + (4 x) + 2" – no, that can't be. Wait, maybe the sign is reversed. Wait, if we have $-4x$, then as a sum, it's $+(-4x)$, so the coefficient is $-4$. So the answer should be $-4$.

Step2: Confirm the rule application

Subtraction of $4x$ (i.e., $-4x$) is equivalent to addition of $-4x$, so when rewriting the expression as a sum of terms, the term $-4x$ is written as $+(-4x)$, so the coefficient of $x$ in that term is $-4$.

Answer:

-4