3x+5/2-1

a) $\frac{x - 5}{4} \geq \frac{3 - 2 x}{5}$

$\Leftrightarrow \frac{5 x - 25}{20} \geq \frac{12 - 8 x}{20}$

$\Leftrightarrow 5 x - 25 \geq 12 - 8 x$

$\Leftrightarrow 5 x + 8 x \geq 12 + 25$

$\Leftrightarrow 13 x \geq 37$

$\Leftrightarrow x \geq \frac{37}{13}$

b) $2 x (6 x - 1) - 3 < 3 x (4 x + 3) - 5 x$

$\Leftrightarrow 12 x^{2} - 2 x - 3 < 12 x^{2} + 9 x - 5 x$

$\Leftrightarrow 12 x^{2} - 12 x^{2} - 2 x - 9 x + 5 x < 3$

$\Leftrightarrow - 6 x < 3$

$\Leftrightarrow x > - \frac{1}{2}$

c) $| x - 4 | = 5 - 3 x$

$\Leftrightarrow [\begin{matrix} 5 - 3 x = x - 4 \\ 5 - 3 x = 4 - x \end{matrix}$

$\Leftrightarrow [\begin{matrix} 5 + 4 = x + 3 x \\ 5 - 4 = - x + 3 x \end{matrix}$

$\Leftrightarrow [\begin{matrix} 4 x = 9 \\ 2 x = 1 \end{matrix}$

$\Leftrightarrow [\begin{matrix} x = \frac{9}{4} \\ x = \frac{1}{2} \end{matrix}$

3x+5/2-1

17/11/2021

By Savannah

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