Solve the compound inequality and graph the solution

x ≤ -3 or 1 < x

Step-by-step explanation:

Solve an inequality the same way you would solve an equation, with one exception. If you multiply or divide by a negative number, the inequality symbol is reversed.

... x + 7 ≤ 4 . . . . . left inequality

... x ≤ -3 . . . . . . . subtract 7 to get the x-term by itself

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... 5 - 3x < 2 . . . . right inequality

... -3x < -3 . . . . . . subtract 5 to get the x-term by itself

... x > 1 . . . . . . . . . divide by -3. Since -3 is negative, we reverse the inequality symbol

The problem statement says the solution is the OR of these, so ...

... x ≤ -3 . . or . . 1 < x

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These are graphed on a number line with a solid dot at -3, and an arrow to the left from there; and an open dot at +1, and an arrow to the right from there. (The dot at 1 is open because x=1 is not in the solution set.)

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Step-by-step explanation: