SOLUTION: Solve the given inequalities and write the solution set using interval notation. -9<2x+7≤19

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Question 1203797: Solve the given inequalities and write the solution set using interval notation. -9<2x+7≤19
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

-9+%3C+2x%2B7%3C=+19

-9-7+%3C+2x%2B7-7%3C=+19-7 Subtracting 7 from all sides.

-16+%3C+2x%3C=+12

-16%2F2+%3C+2x%2F2%3C=+12%2F2 Dividing all sides by 2.

-8+%3C+x%3C=+6

That condenses to the interval notation (-8, 6]

Use a curved parenthesis to exclude the endpoint -8.
Use a square bracket to include the endpoint 6.

The graph on a number line will have an open hole at -8 and a closed filled in endpoint at 6. Shade in between.

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve the given inequality and write the solution set using interval notation. -9 < 2x+7 ≤ 19
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You are given a compound inequality

    -9 < 2x+7 ≤ 19.


Subtract  7  from all  3  parts of this compound inequality.  You will get an equivalent compound inequality

    -9 - 7 <  2x  <=  19 - 7,

or

    -16 < 2x <= 12.


Now divide by  2  all  3  parts the last compound inequality.  You will get an equivalent compound inequality

     -8 < x < = 6.


It is your answer: The solution to the original inequality is the interval (-8,6] of the number line.

Left endpoint is not included, while right endpoint is included to the solution set.

Solved.