Solve the following compound inequality: −2(x + 4) + 10 3 < x − 7 or −2x + 9 > (x + 8) a x < 3 or x > −3 b x > 3 or x < −3 c x < 7 or x > −3 d x > 7 or x < −3

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MrRoyal MrRoyal · Answer 1 · 2022-08-26T12:24:12+02:00

The solution to the compound inequality is x > 3 or x < 1/3

The compound inequality is given as:

−2(x + 4) + 10 < x − 7 or −2x + 9 > (x + 8)

Start by opening the brackets

−2x - 8 + 10 < x − 7 or −2x + 9 > x + 8

Next, we evaluate the like terms in the individual inequality

−3x < − 9 or −3x > -1

Next, we divide the through the individual inequalities by the coefficient of x.

−3x/-3 < − 9/-3 or −3x/-3 > -1/-3

Evaluate the quotients

x > 3 or x < 1/3

Hence, the solution to the compound inequality is x > 3 or x < 1/3