Solve the following inequation- 1-23 x-2-4 -1-3x-6- x - R-4 MARKS-

Steps: 2 Marks Calculations: 1 Mark Answer: 1 Mark 1/2 ( 3x/2+4 )≥1/3(x 6), xϵ R ⇒1/2 ( 3x+8/2 )≥1/3(x 6) ⇒3x/4+2≥x/3 2 ⇒3x+8/4≥x 6/3 ⇒ 9x+24≥ 4x 24 ⇒ 9x 4x≥ ...

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Standard X

Mathematics

Multiplying/Dividing a Negative Entity

Solve the fol...

Question

Solve the following inequation: $\frac{1}{2} (\frac{3 x}{2} + 4) \geq \frac{1}{3} (x - 6), x ϵ R$
[4 MARKS]

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Solution

Steps: 2 Marks
Calculations: 1 Mark
Answer: 1 Mark

$\frac{1}{2} (\frac{3 x}{2} + 4) \geq \frac{1}{3} (x - 6), x ϵ R \Rightarrow \frac{1}{2} (\frac{3 x + 8}{2}) \geq \frac{1}{3} (x - 6) \Rightarrow \frac{3 x}{4} + 2 \geq \frac{x}{3} - 2 \Rightarrow \frac{3 x + 8}{4} \geq \frac{x - 6}{3} \Rightarrow 9 x + 24 \geq 4 x - 24 \Rightarrow 9 x - 4 x \geq - 24 - 24 \Rightarrow 5 x \geq - 48 \Rightarrow x \geq \frac{- 48}{5}, x ϵ R$

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Solve the following inequation: 12(3x2+4)≥13(x−6),xϵR [4 MARKS]

Steps: 2 Marks Calculations: 1 Mark Answer: 1 Mark 12(3x2+4)≥13(x−6),xϵR⇒12(3x+82)≥13(x−6)⇒3x4+2≥x3−2⇒3x+84≥x−63⇒9x+24≥4x−24⇒9x−4x≥−24−24⇒5x≥−48⇒x≥−485,xϵR

Solve the following inequation: $\frac{1}{2} (\frac{3 x}{2} + 4) \geq \frac{1}{3} (x - 6), x ϵ R$
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