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Simplify the following expression: \[ 8-14\{x-8[3-5(2 x-3)+3 x]-14\} \] \( =\square \) E \( x+\square \) If the answer is negative, put the negative sign as well

Ask by Clark Park. in Canada
Mar 10,2025

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Tutor-Verified Answer

Answer

The simplified expression is \(2220 - 798x\).

Solution

Calculate or simplify the expression \( 8-14\{x-8[3-5(2x-3)+3x]-14\} \). Simplify the expression by following steps: - step0: Solution: \(8-14\left(x-8\left(3-5\left(2x-3\right)+3x\right)-14\right)\) - step1: Calculate: \(8-14\left(x-8\left(18-7x\right)-14\right)\) - step2: Subtract the terms: \(8-14\left(57x-158\right)\) - step3: Expand the expression: \(8-798x+2212\) - step4: Add the numbers: \(2220-798x\) The simplified expression is \(2220-798x\).

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The Deep Dive

To simplify the expression \( 8 - 14\{x - 8[3 - 5(2x - 3) + 3x] - 14\} \), we will start from the innermost brackets and work our way out: 1. Begin with \( 5(2x - 3) = 10x - 15 \). 2. Now substitute and simplify the expression within the brackets: \[ 3 - (10x - 15) + 3x = 3 + 15 - 10x + 3x = 18 - 7x. \] 3. Next, substitute this back into the expression: \[ 8 - 14\{x - 8(18 - 7x) - 14\}. \] 4. Simplifying \( 8(18 - 7x) = 144 - 56x\), we get: \[ x - 144 + 56x - 14 = 57x - 158. \] 5. Now substitute: \[ 8 - 14(57x - 158) = 8 - 798x + 2212. \] 6. Finally, combine the constant terms: \[ 2212 + 8 = 2220. \] Thus, the final simplified expression is: \[ -798x + 2220. \] So we have: \( = -798 E x + 2220 \)

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