How do you solve the inequality $-2x + 3 >7$ ?

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Answer 1 · 2015-12-03T12:59:55

$x < -2$

To solve a linear inequality, you can mostly behave the same way as you do when solving linear equations, with two important equations:

each time you multiply both sides with a negative number or if you divide both sides by a negative number, you need to "turn" the greater/less sign, so, transform $<$ into $>$ and vice versa
if you flip the sides of the equation, you also need to "turn" the greater/less sign.

With this knowledge, you can solve the inequality as follows:

$-2< + 3 > 7$

... add $-3$ on both sides ...

$-2x > 4$

... divide by $-2$ on both sides; don't forget to flip the inequality sign!

$x < -2$

So, the solution is $x < -2$ .

How do you solve the inequality -2x + 3 >7-2x + 3 >7?