Question

Solve the following compound inequality: (1 point)

-2(x+8) +6 > x-4 or -3x + 12 < 6(x-4)
0x<2 orx>4
Ox>2 orx<4
0x<-2 orx>4
Ox>-2 orx<44

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 ❞