Math / Algebra

QuestionSimplify by first removing the parentheses and then combining the like terms. $10(x+1)-2(5 x-3)$ $\square$ Need Help? Read It Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to simplify an expression by getting rid of parentheses and then grouping similar terms. Watch out! Don't forget to distribute correctly, especially with that negative sign in front of the second parentheses – it's a sneaky one!

STEP 2

1. Distribute
2. Combine

STEP 3

Alright, let's kick things off by distributing the $\bf{10}$ across the $(x+1)$ .
Remember, this means multiplying $\bf{10}$ by both $\bf{x}$ and $\bf{1}$ .
This gives us $10 \cdot x + 10 \cdot 1 = 10x + 10.$

STEP 4

Next up, we'll distribute the $\bf{-2}$ across $(5x - 3)$ .
It's super important to remember that we're distributing $\bf{-2}$ , not just $\bf{2}$ !
This gives us $-2 \cdot 5x + (-2) \cdot (-3) = -10x + 6.$

STEP 5

Now, let's put it all together.
We had $10x + 10$ from the first distribution and $-10x + 6$ from the second.
So, our expression becomes $10x + 10 - 10x + 6.$

STEP 6

Time to combine like terms!
We've got some $x$ terms and some constant terms.
Let's start with the $x$ terms: $10x$ and $-10x$ .
Adding those together gives us $10x - 10x = (10-10)x = 0x = 0.$ So, the $x$ terms add to zero and disappear!

STEP 7

Now for the constant terms: $10$ and $6$ .
Adding those together gives us $10 + 6 = 16.$

STEP 8

Putting it all together, we have $0$ (from the $x$ terms) plus $16$ (from the constant terms), which gives us a final simplified expression of $16$ .

STEP 9

Our final simplified expression is $16$ .

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QuestionSimplify by first removing the parentheses and then combining the like terms. $10(x+1)-2(5 x-3)$ $\square$ Need Help? Read It Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to simplify an expression by getting rid of parentheses and then grouping similar terms. Watch out! Don't forget to distribute correctly, especially with that negative sign in front of the second parentheses – it's a sneaky one!

STEP 2

1. Distribute
2. Combine

STEP 3

Alright, let's kick things off by distributing the $\bf{10}$ across the $(x+1)$ .
Remember, this means multiplying $\bf{10}$ by both $\bf{x}$ and $\bf{1}$ .
This gives us $10 \cdot x + 10 \cdot 1 = 10x + 10.$

STEP 4

Next up, we'll distribute the $\bf{-2}$ across $(5x - 3)$ .
It's super important to remember that we're distributing $\bf{-2}$ , not just $\bf{2}$ !
This gives us $-2 \cdot 5x + (-2) \cdot (-3) = -10x + 6.$

STEP 5

Now, let's put it all together.
We had $10x + 10$ from the first distribution and $-10x + 6$ from the second.
So, our expression becomes $10x + 10 - 10x + 6.$

STEP 6

Time to combine like terms!
We've got some $x$ terms and some constant terms.
Let's start with the $x$ terms: $10x$ and $-10x$ .
Adding those together gives us $10x - 10x = (10-10)x = 0x = 0.$ So, the $x$ terms add to zero and disappear!

STEP 7

Now for the constant terms: $10$ and $6$ .
Adding those together gives us $10 + 6 = 16.$

STEP 8

Putting it all together, we have $0$ (from the $x$ terms) plus $16$ (from the constant terms), which gives us a final simplified expression of $16$ .

STEP 9

Our final simplified expression is $16$ .

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QuestionSimplify by first removing the parentheses and then combining the like terms. 10(x+1)−2(5x−3)10(x+1)-2(5 x-3)10(x+1)−2(5x−3) □\square□ Need Help? Read It Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to simplify an expression by getting rid of parentheses and then grouping similar terms. Watch out! Don't forget to distribute correctly, especially with that negative sign in front of the second parentheses – it's a sneaky one!

STEP 2

1. Distribute2. Combine

STEP 3

Alright, let's **kick things off** by distributing the 10\bf{10}10 across the (x+1)(x+1)(x+1).Remember, this means multiplying 10\bf{10}10 by *both* x\bf{x}x and 1\bf{1}1.This gives us 10⋅x+10⋅1=10x+10.10 \cdot x + 10 \cdot 1 = 10x + 10.10⋅x+10⋅1=10x+10.

STEP 4

Next up, we'll distribute the −2\bf{-2}−2 across (5x−3)(5x - 3)(5x−3).It's super important to remember that we're distributing −2\bf{-2}−2, not just 2\bf{2}2!This gives us −2⋅5x+(−2)⋅(−3)=−10x+6.-2 \cdot 5x + (-2) \cdot (-3) = -10x + 6.−2⋅5x+(−2)⋅(−3)=−10x+6.

STEP 5

Now, let's put it all together.We had 10x+1010x + 1010x+10 from the first distribution and −10x+6-10x + 6−10x+6 from the second.So, our expression becomes 10x+10−10x+6.10x + 10 - 10x + 6.10x+10−10x+6.

STEP 6

STEP 7

Now for the constant terms: 101010 and 666.Adding those together gives us 10+6=16.10 + 6 = 16.10+6=16.

STEP 8

Putting it all together, we have 000 (from the xxx terms) plus 161616 (from the constant terms), which gives us a **final simplified expression** of 161616.

STEP 9

Our final simplified expression is 161616.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSimplify by first removing the parentheses and then combining the like terms. $10(x+1)-2(5 x-3)$ $\square$ Need Help? Read It Submit Answer

1. Distribute
2. Combine

Alright, let's kick things off by distributing the $\bf{10}$ across the $(x+1)$ .
Remember, this means multiplying $\bf{10}$ by both $\bf{x}$ and $\bf{1}$ .
This gives us $10 \cdot x + 10 \cdot 1 = 10x + 10.$

Next up, we'll distribute the $\bf{-2}$ across $(5x - 3)$ .
It's super important to remember that we're distributing $\bf{-2}$ , not just $\bf{2}$ !
This gives us $-2 \cdot 5x + (-2) \cdot (-3) = -10x + 6.$

Now, let's put it all together.
We had $10x + 10$ from the first distribution and $-10x + 6$ from the second.
So, our expression becomes $10x + 10 - 10x + 6.$

Now for the constant terms: $10$ and $6$ .
Adding those together gives us $10 + 6 = 16.$

Putting it all together, we have $0$ (from the $x$ terms) plus $16$ (from the constant terms), which gives us a final simplified expression of $16$ .

Our final simplified expression is $16$ .