Solve- 2x-13-3x-24-2-x5

2x 13≥3x 24 2 x5 #160; ⇒2x 13≥15x 10 8+4x20 ⇒2x 13≥19x 1820 ⇒ 40x 20≥ 57x 54 ⇒ 40x 20 57x≥ 57x 54 57x ⇒ 17x 20≥ 54 ⇒ 17x ...

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Standard VIII

Mathematics

Numbers in General Form

Solve: 2x-13...

Question

Solve: $\frac{2 x - 1}{3} \geq \frac{3 x - 2}{4} - \frac{2 - x}{5}$

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Solution

$\frac{2 x - 1}{3} \geq \frac{3 x - 2}{4} - \frac{2 - x}{5}$
$\Rightarrow \frac{2 x - 1}{3} \geq \frac{15 x - 10 - 8 + 4 x}{20}$
$\Rightarrow \frac{2 x - 1}{3} \geq \frac{19 x - 18}{20}$
$\Rightarrow 40 x - 20 \geq 57 x - 54$
$\Rightarrow 40 x - 20 - 57 x \geq 57 x - 54 - 57 x$
$\Rightarrow - 17 x - 20 \geq - 54$
$\Rightarrow - 17 x - 20 + 20 \geq - 54 + 20$
$\Rightarrow - 17 x \geq - 34$
$\Rightarrow 17 x \leq 34$
$\Rightarrow x \leq \frac{34}{17} = 2$
$∴ x \leq 2$
$∴ x \in (- \infty, 2]$

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Solve:2x−13≥3x−24−2−x5

2x−13≥3x−24−2−x5 ⇒2x−13≥15x−10−8+4x20⇒2x−13≥19x−1820⇒40x−20≥57x−54⇒40x−20−57x≥57x−54−57x⇒−17x−20≥−54⇒−17x−20+20≥−54+20⇒−17x≥−34⇒17x≤34⇒x≤3417=2∴x≤2∴x∈(−∞,2]

Solve: $\frac{2 x - 1}{3} \geq \frac{3 x - 2}{4} - \frac{2 - x}{5}$