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Solve and graph the absolute value inequality: |2x + 1| ≤ 5. number line with closed dots on negative 3 and 2 with shading going in the opposite directions. number line with closed dots on negative 3 and 2 with shading in between. number line with open dots on negative 3 and 2 with shading in between. number line with closed dots on negative 2 and 2 with shading in between.
Hint: |ax + b| ≤ c is equivalent to -c ≤ ax + b ≤ c
What????? So confused. Could you explain better?
In order to properly graph the absolute value inequality, you must first solve for x. The hint I gave you shows a mathematical statement equivalent to the given statement that allows you to solve for x, which in turn, will enable you to properly graph the inequality.
ok, so |2x + 1| ≤ 5. First, would i subtract one from each side?
Set up two equations We know 2x+1≤5 and 2x+1≥−5 Solve for each \[\huge~2x+1≤5 \] \[\huge~2x+1≥−5\]
2x+1<5 -1 -1 2x <4 /2 /2 x<2? for the first one?
2x+1>5 -1 -1 2x > 4 /2 /2 x>2 for the second one as well?
It's much easier to solve it as just one compound inequality: -5 ≤ 2x + 1 ≤ 5 Subtract one from each side, then divide each side by two.
with the line underneath the signs
-6 ≤ 2x ≤ 4 Then divide each side by 2.
with lines underneath
-3 ≤ x ≤ 2
The inequality basically states that the solution, x, exists between -3 and 2 (inclusive)
thank you so much!