How do you solve $5 v + 10 \leq - 4 v - 17 < 9 - 2 v$ $5v + 10<= - 4v - 17< 9- 2v$ ?

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How do you solve $5 v + 10 \leq - 4 v - 17 < 9 - 2 v$ $5v + 10<= - 4v - 17< 9- 2v$ ?

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Answer 1 · 2017-04-17T13:26:34

$- 13 < v \leq - 3$ $-13 < v <=- 3$

Explanation:

Break the inequality into 2 parts and solve each separately.

$5 v + 10 \leq - 4 v - 17 < 9 - 2 v$ $color(blue)(5v +10 <= -4v -17) < 9-2v$
$5 v + 10 \leq - 4 v - 17 < 9 - 2 v$ $5v +10 <= color(red)(-4v -17 < 9-2v)$

$5 v + 10 \leq - 4 v - 17$ $color(blue)(5v +10 <= -4v -17)$
$10 + 17 \leq - 4 v - 5 v$ $color(blue)(10+17 <= -4v-5v)$
$27 \leq - 9 v \div - 9 \leftarrow$ $color(blue)(27<=-9v)" "div -9" "larr$ change sign around
$- 3 \geq v$ $color(blue)(-3 >=v)$

$- 4 v - 17 < 9 - 2 v$ $color(red)(-4v -17 < 9-2v)$
$- 17 - 9 < - 2 v + 4 v$ $color(red)(-17 -9 <-2v+4v)$
$- 26 < 2 v$ $color(red)(-26 <2v)$
$- 13 < v$ $color(red)(-13 < v)$

Combine the two solutions for v:
$- 13 < v and v \leq - 3$ $color(red)(-13 < v)" and "color(blue)(v<=-3)$

$- 13 < v \leq - 3$ $color(red)(-13 <) v color(blue)(<= -3)$

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How do you solve $5 v + 10 \leq - 4 v - 17 < 9 - 2 v$ $5v + 10<= - 4v - 17< 9- 2v$ ?

1 Answer

Explanation:

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How do you solve 5v+10≤−4v−17<9−2v5v + 10<= - 4v - 17< 9- 2v?

1 Answer

Explanation:

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How do you solve $5 v + 10 \leq - 4 v - 17 < 9 - 2 v$ $5v + 10<= - 4v - 17< 9- 2v$ ?