Solve the compound Inequalities, graph the solutions and write the solutions in interval notation. Show all work.-5<2x+3 less then or equal to 11

Question

asked Feb 19, 2023 15.1k views

1 Answer

Mouhong Lin · Answer 1 · 2023-02-24T05:10:19+0000

Answer:

Interval Notation: (-4,4]

Step-by-step explanation:

Given the compound inequality:

$-5<2x+3\le11$

Subtract 3 from all sides of the inequality:

$\begin{gathered} -5-3<2x+3-3\le11-3 \\ -8<2x\le8 \end{gathered}$

Next, divide all sides of the inequality by 2.

$\begin{gathered} (-8)/(2)<(2x)/(2)\le(8)/(2) \\ -4The solution to the compound inequality in interval notation is:[tex](-4,4\rbrack$

Next, we graph the solution.

• Since we have, -4,• At, x≤4,, we use a ,closed circle,.

The graph is shown below: