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2 The following inequality is given: \( 3(x+7)<\frac{x}{2}+1 \) 2.2.1 Solve for \( x \) in the inequality.

Ask by Mccoy Mccarthy. in South Africa
Nov 14,2024

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\( x<-8 \).

Solución

Solve the equation \( 3(x+7)<\frac{x}{2}+1 \). Solve the inequality by following steps: - step0: Solve for \(x\): \(3\left(x+7\right)<\frac{x}{2}+1\) - step1: Multiply both sides: \(3\left(x+7\right)\times 2<\left(\frac{x}{2}+1\right)\times 2\) - step2: Multiply the terms: \(6x+42

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The Deep Dive

To solve the inequality \( 3(x+7)<\frac{x}{2}+1 \), first distribute the 3 on the left side: \( 3x + 21 < \frac{x}{2} + 1 \). Next, eliminate the fraction by multiplying the whole inequality by 2: \( 2(3x + 21) < x + 2 \) This simplifies to: \( 6x + 42 < x + 2 \). Now, rearrange the inequality by subtracting \( x \) from both sides: \( 6x - x + 42 < 2 \) Which simplifies to: \( 5x + 42 < 2 \). Next, subtract 42 from both sides: \( 5x < 2 - 42 \) Thus, \( 5x < -40 \). Finally, divide by 5: \( x < -8 \). So the solution to the inequality is \( x < -8 \).

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