Simplify the expression. − 3 [ 2 x − ( 4 − x ) ] -3[2x-(4-x)]

Here we're asked to simplify the expression that negative three times two X minus four minus X. So getting started with our steps here, the first thing we want to do is distribute any constants or variables into parentheses. Now I actually have two instances of parentheses here. So there are two places in which I need to distribute and you need to be really careful here just because of the way in which we need to distribute. So I have this negative three on the outside of these square brackets here. That means it needs to get distributed to this term, negative two x, and also to this larger term, negative four minus x, which also is enclosed in parentheses within these square brackets. So when doing this distribution here, that first term, it's pretty straightforward. Negative three times two x is going to give me a negative six x. And then when I distribute my negative three to my next term, I need to make sure I'm multiplying it by that negative right there. So negative three times negative one is going to give me a positive three and that positive three is multiplying what's in parentheses there, four minus x. So I'm gonna have to distribute again here by taking this three and distributing it now into these parentheses. So keeping that negative six x here and then three times four will give me 12, so plus 12. And then distributing it to that negative x is going to give me negative three x. So we kind of had to do a double distribution there, which can get a bit tricky. So make sure that you stay organized. So moving on to our second step here, we want to identify our like terms. Now Now I see two terms with a variable here and that variable is x in both cases. So negative six x and negative three x. These are the same variable x raised to the same exponent, one which is implied when there is no exponent. Then I have that constant 12, which I don't have any other constants, so I don't have to worry about doing anything else there. So having identified my like terms, I now wanna group them by writing them next to each other. So negative six x minus three x and then that positive 12 just on the end here. So moving on to my final step here, combining my like terms by adding or subtracting their coefficients. I have negative six x and a negative three x. That's going to be negative nine x. And then that positive 12, I don't need to do anything with because it doesn't have any other like terms. So this is my fully simplified expression, negative nine x plus 12. Now this was a tricky one, so great job. I'll see you in the next one to keep practicing.

1. Review of Real Numbers

Simplifying Expressions

Intermediate Algebra

1. Review of Real Numbers

Simplifying Expressions

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Multiple Choice

Simplify the expression.
$- 3 [2 x - (4 - x)]$

$- 9 x + 12$

$- 3 x + 12$

$9 x minus 12$

$3 x minus 12$

Verified step by step guidance

Start by examining the expression: $-3[2x - (4 - x)]$. Notice that there is a subtraction of a quantity inside the brackets, so the first step is to simplify inside the brackets.

Distribute the negative sign inside the parentheses: rewrite \$2x - (4 - x)$ as $2x - 4 + x$. This is because subtracting a quantity is the same as subtracting each term inside it.

Combine like terms inside the brackets: \$2x + x$ becomes $3x$, so the expression inside the brackets simplifies to $3x - 4$.

Now the expression is $-3[3x - 4]$. Next, distribute the $-3$ across each term inside the brackets: multiply $-3$ by \$3x$ and $-3$ by $-4$ separately.

Write the result of the distribution as $-3 \times 3x + (-3) \times (-4)$, which simplifies to $-9x + 12$. This is the simplified form of the original expression.

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Simplify the expression.−3[2x−(4−x)]-3[2x-(4-x)]

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Simplify the expression.
$- 3 [2 x - (4 - x)]$