How do you solve $7 > 1 - 2 x \leq 10$ $7>1-2x<=10$ ?

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How do you solve $7 > 1 - 2 x \leq 10$ $7>1-2x<=10$ ?

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Answer 1 · 2015-05-27T13:12:21

Split the compound inequality into 2 simple inequalities;
simplify each;
re-combine

$7 > 1 - 2 x \leq 10$ $7>1-2x<=10$

Inequality Part 1:
$7 > 1 - 2 x$ $7>1-2x$
$\to 2 x > - 6$ $rarr 2x > -6$
$\to x > - 3$ $rarr x> -3$

Inequality Part 2:
$1 - 2 x \leq 10$ $1-2x<=10$
$\to - 9 \leq 2 x$ $rarr -9 <= 2x$
$\to x \geq - \frac{9}{2}$ $rarr x>= -9/2$

Recombining:
$x > - 3$ $x> -3$ and $x \geq - \frac{9}{2}$ $x>=-9/2$
simplifies to
$x > - 3$ $x > -3$ (since if $x > - 3 \to x \geq - \frac{9}{2}$ $x> -3 rarr x>= -9/2$ )

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How do you solve $7 > 1 - 2 x \leq 10$ $7>1-2x<=10$ ?

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