Free solve the following compound inequality: −2(x + 4) + 10 < x − 7 or −2x + 9 > 3(x + 8) x < 3 or x > −3 x > 3 or x < −3 x < 7 or x > −3 x > 7 or x < −3

Let's solve the first inequality at first. So,

−2(x + 4) + 10 < x − 7

-2x- 8 + 10 < x - 7 By distribution property.

-2x + 2 < x - 7 Adding the like terms.

-2x < x - 7 - 2 Subtract 2 from each sides.

-2x < x - 9 By simplifying.

-2x - x < -9 Subtract x from each sides.

-3x < -9

Since we are dividing by negative 3. So, sign of inequality will get change.

So, x>3

Now the next inequality is,

−2x + 9 > 3(x + 8)

-2x + 9 > 3x + 24

-2x > 3x + 24 - 9

-2x > 3x + 15

-2x - 3x > 15

-5x >15

So, x <-3

Hence, the correct choice is x > 3 or x < −3.

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