Question

Solve the following compound inequality: (1 point)

Answer 1

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \: x < -2 \:\: or \:\; x >4$

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$\large \tt Solution \: :$

$\textsf{First Inequality :}$

$\qquad \tt \rightarrow \: - 2(x + 8) + 6 > x - 4$

$\qquad \tt \rightarrow \: - 2x - 16 + 6 > x - 4$

$\qquad \tt \rightarrow \: - 2x - 10 > x - 4$

$\qquad \tt \rightarrow \: - 10 + 4 > x + 2x$

$\qquad \tt \rightarrow \: - 6 > 3x$

$\qquad \tt \rightarrow \: - \cfrac{ 6}{3} > x$

$\qquad \tt \rightarrow \: - 2 > x$

$\qquad \tt \rightarrow \: \therefore x < - 2$

$\textsf{Second Inequality :}$

$\qquad \tt \rightarrow \: - 3x + 12 < 6(x - 4)$

$\qquad \tt \rightarrow \: - 3x + 12 < 6x - 24$

$\qquad \tt \rightarrow \: 12 + 24 < 6x + 3x$

$\qquad \tt \rightarrow \: 36 < 9x$

$\qquad \tt \rightarrow \: \cfrac{36}{9} < x$

$\qquad \tt \rightarrow \: 4 < x$

$\qquad \tt \rightarrow \: \therefore x > 4$

Answered by : ❝ AǫᴜᴀWɪᴢ ❞