Question
Simplify \( 8+3\{x-2[x+5(x+3)]\} \) \( 33 x-82 \) \( -33 x+82 \) \( -33 x-82 \)
Ask by Robbins Hamilton. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( -33x - 82 \).
Solution
Let's simplify the expression step by step.
The expression to simplify is:
8 + 3{x - 2[x + 5(x + 3)]}
Step 1. Simplify inside the inner brackets:
Inside the square brackets, we have:
x + 5(x + 3)
Distribute the 5:
= x + 5x + 15
Combine like terms:
= 6x + 15
Step 2. Substitute back into the expression:
Now, the expression becomes:
8 + 3{x - 2(6x + 15)}
Step 3. Distribute the -2 inside the curly brackets:
Multiply -2 with (6x + 15):
= -12x - 30
So inside the curly brackets we get:
x - 12x - 30 = -11x - 30
Step 4. Multiply by 3 and then add 8:
Now, multiply by 3:
3(-11x - 30) = -33x - 90
Then add the 8:
8 - 33x - 90 = -33x - 82
Thus, the expression simplifies to:
-33x - 82
Comparing with the provided options, the correct answer is:
-33 x -82
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Simplify this solution Beyond the Answer
To simplify the expression \( 8 + 3\{x - 2[x + 5(x + 3)]\} \), we first need to work inside the curly brackets. 1. Start with the innermost expression: \( 5(x + 3) = 5x + 15 \). 2. Then, calculate \( x + 5(x + 3) = x + 5x + 15 = 6x + 15 \). 3. Now, focus on \( 2[x + 5(x + 3)] = 2(6x + 15) = 12x + 30 \). 4. Substitute this back into the curly brackets: \( x - (12x + 30) = x - 12x - 30 = -11x - 30 \). 5. Next, multiply by 3: \( 3(-11x - 30) = -33x - 90 \). 6. Finally add the 8: \( 8 + (-33x - 90) = -33x - 82 \). So the simplified expression is \( -33x - 82\). That's the final result!
