Answer: Choice F) [tex]x \le -5[/tex]
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Explanation:
One long rectangle represents x. Four of them represent 4x
One tiny unshaded square represents a unit 1. Specifically this value is positive. We have 2 columns and 6 rows, so there are 2*6 = 12 tiny squares.
So the stuff in the first box (the four long rectangles and the 12 tiny unshaded squares) represent the expression 4x+12
The stuff in the second box is -8 since we have 8 shaded squares each shaded square being -1.
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The inequality we need to solve is [tex]4x+12 \le -8[/tex]
We'll subtract 12 from both sides, then divide both sides by 4 to fully isolate x
This is what the steps would look like:
[tex]4x+12 \le -8\\\\\\4x+12-12 \le -8-12 \ \text{ subtract 12 from both sides}\\\\\\4x \le -20\\\\\\\frac{4x}{4} \le \frac{-20}{4} \ \text{ Divide both sides by 4}\\\\\\x \le -5\\\\\\[/tex]
The inequality sign does not flip since we did not divide both sides by a negative number.
