PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
10th Edition
ISBN: 9780136174318
Author: Demana
Publisher: PEARSON
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Chapter P, Problem 59RE
Solution

The solution of the inequality −2<x+4≤7 and draw the solution graph on a number line.

The solution of the inequality is −6,3 .

The graph is solution set is shown below

  PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA), Chapter P, Problem 59RE , additional homework tip 1

Given:

The inequality, −2<x+4≤7 .

Concept Used:

  • If there is the strict inequality symbol < or> , then use a parenthesis on the interval
  • If there is the inequality symbol ≤ or≥ , then use a bracket on the interval
  • To graph the endpoint with strict inequality < or>, use the open parenthesis or a hollow circle at that endpoint.
  • To graph the endpoint with inequality symbol ≤ or≥, use the bracket or a solid circle at that endpoint.

Calculation:

In order to solve the given inequality −2<x+4≤7 , add 4 to both sides and simplify further as shown below

  −2<x+4≤7−2−4<x+4−4≤7−4−6<x≤3

Therefore, the solution of the inequality is −6<x≤3 or −6,3 .

The solution of the inequality is all real number that are greater than −6 and less than or equal to 3. Since the inequality sign is strict with −6 , use a hollow circle at −6 and a solid circle at the right endpoint 3as shown in below graph,

  PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA), Chapter P, Problem 59RE , additional homework tip 2

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Chapter P Solutions

PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)

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