Question
Simplify the following expression: \[ 5-14\{x-8[3-5(2 x-3)+3 x]-13\} \] \( =\square \) E \( x+\square \) If the answer is negative, put the negative sign as well
Ask by Fernandez Cross. in Canada
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(2203 - 798x\).
Solution
Calculate or simplify the expression \( 5-14\{x-8[3-5(2x-3)+3x]-13\} \).
Simplify the expression by following steps:
- step0: Solution:
\(5-14\left(x-8\left(3-5\left(2x-3\right)+3x\right)-13\right)\)
- step1: Calculate:
\(5-14\left(x-8\left(18-7x\right)-13\right)\)
- step2: Subtract the terms:
\(5-14\left(57x-157\right)\)
- step3: Expand the expression:
\(5-798x+2198\)
- step4: Add the numbers:
\(2203-798x\)
The simplified expression is \(2203-798x\).
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Simplify this solution The Deep Dive
Let's simplify the given expression step by step: Starting with: \[ 5 - 14\{x - 8[3 - 5(2x - 3) + 3x] - 13\} \] First, simplify inside the innermost brackets: \[ 5(2x - 3) = 10x - 15 \] Now replace it in the expression: \[ 3 - (10x - 15) + 3x = 3 - 10x + 15 + 3x = 18 - 7x \] Now replace this back into the expression: \[ 8[18 - 7x] = 144 - 56x \] Then insert back into the main expression: \[ 5 - 14\{x - (144 - 56x) - 13\} \] \[ = 5 - 14\{x - 144 + 56x - 13\} \] \[ = 5 - 14\{57x - 157\} \] Now distribute the -14: \[ 5 - 798x + 2198 = -798x + 2203 \] Thus, the final simplified expression is: \[ = -798x + 2203 \] So, in the given format: \( = -798 \ E \ x + 2203 \)
