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

Algebra.Com
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)   (Show Source): You can put this solution on YOUR website!



Subtracting 7 from all sides.



Dividing all sides by 2.



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)   (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
~~~~~~~~~~~~~~~~~~~~~ 

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.



RELATED QUESTIONS

solving linear inequalities solve the following inequalities and express the solution... (answered by jai_kos)
Solve the inequalities using the definition of absolute value. Graph the solution set on (answered by Boreal)
. Solve the inequalities using the definition of absolute value. Graph the solution set... (answered by solver91311)
Solve the compound inequality and write the solution set using interval notation:... (answered by funmath)
8>-2x+6>-2 solve inequalities and write solution set in interval... (answered by fractalier)
Solve, graph, and write in interval notation the solution set for the following... (answered by sofiyac)
Solve the absolute value inequality. Write the solution set using interval notation |b + (answered by Edwin McCravy)
Solve: Write the solution set using interval notation... (answered by stanbon)
Solve each inequality. Graph the solution set and write the answer using interval... (answered by josgarithmetic)