What is the expression 4+8(3x−2)−7x

Question

What is the expression 4+8(3x−2)−7x
4
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8
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3
𝑥
−
2
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−
7
𝑥
 when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work.(4 points).............

GPT-4o mini · Answer

To simplify the expression $ 4 + 8(3x - 2) - 7x $, we'll follow the order of operations and apply the distributive property. ### Step 1: Distribute the 8 First, we need to distribute the $ 8 $ into the parentheses: $$ 8(3x - 2) = 8 \cdot 3x + 8 \cdot (-2) = 24x - 16 $$ ### Step 2: Rewrite the Expression Now we can rewrite the original expression substituting the distributed result: $$ 4 + (24x - 16) - 7x $$ ### Step 3: Combine Like Terms Next, we combine the like terms. First, we can rearrange and combine the $ x $ terms and the constant terms: $$ = 4 - 16 + 24x - 7x $$ Combine the constant terms: $$ 4 - 16 = -12 $$ Now combine the $ x $ terms: $$ 24x - 7x = 17x $$ ### Step 4: Write the Final Expression Putting it all together: $$ -12 + 17x $$ Thus, the expression $ 4 + 8(3x - 2) - 7x $ simplifies to: $$ \boxed{17x - 12} $$

Gir · Answer

how would i type that with showing my work?.

GPT-4o mini · Answer

Certainly! Here’s how you can present your work step-by-step in a clear and organized manner. You can use this structure for typing out the solution:

Given Expression: \[ 4 + 8(3x - 2) - 7x \]

Step 1: Apply the Distributive Property Distribute $ 8 $ into the parentheses $ (3x - 2) $: \[ 8(3x - 2) = 8 \cdot 3x + 8 \cdot (-2) = 24x - 16 \]

Step 2: Rewrite the Expression Substituting the result of the distribution back into the expression: \[ 4 + (24x - 16) - 7x \]

Step 3: Combine Like Terms Rearranging and combining the terms:

Combine the constant terms: \[ 4 - 16 = -12 \]
Combine the $ x $ terms: \[ 24x - 7x = 17x \]

Step 4: Final Expression Putting it all together, we have: \[ -12 + 17x \] This can also be written as: \[ \boxed{17x - 12} \]

You can type it in any document or online platform, using math formatting to present equations clearly (like using LaTeX for online forums). If you're typing in a plain text document, simply use standard symbols and clear explanations for each step.

Gir · Answer

can you write it with just the numbers showing your work pls.

GPT-4o mini · Answer

Sure! Here’s a more concise version of the solution, focusing solely on the numbers and calculations, presenting the work step-by-step:

1. Start with the expression: \[ 4 + 8(3x - 2) - 7x \]

2. Distribute the $8$: \[ = 4 + (8 \cdot 3x) + (8 \cdot -2) - 7x \] \[ = 4 + 24x - 16 - 7x \]

3. Combine constant terms: \[ = (4 - 16) + (24x - 7x) \] \[ = -12 + 17x \]

4. Final expression: \[ = 17x - 12 \]

You can use this format in documents or homework assignments to show your work clearly and concisely while maintaining the focus on the numerical calculations.