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What is the graph of the solution to the following compound inequality?
5x-1 < 19 and -3 - x+1 <1
A
B
C
D

1 Point What is the graph of the solution to the following compound inequality? 5x-example-1
User Vegeta
by
7.8k points

2 Answers

1 vote

Answer:

The correct graph of the solution to the given compound inequality is:

C

Explanation:

  • The first inequality is given by:


5x-1<19

on adding 1 on both the side of the inequality we have:


5x<20

on dividing both side of the inequality by 5 we have:


x<(20)/(5)\\\\x<4

The graph of this inequality is the shaded region to the left of 4 with a open circle at 4( since the inequality is strict)

  • The second inequality is:


-3-x+1\leq 1\\\\-3+1-x\leq 1\\\\-2-x\leq 1\\\\-2-1\leq x\\\\x\geq -3

The graph of this inequality is the shaded region to the right of -3 and closed circle at -3 ( since the inequality is not strict i.e. a inequality with a equality sign )

Hence, the graph of the compound inequality is the set of all the points between -3 and 4 including -3 and excluding 4.

User DazWorrall
by
8.6k points
2 votes

Answer:

Option C

Explanation:

The given inequality is

5x-1 < 19 and
-3-x+1\le1

Group similar terms to get:

5x < 19+1 and
-x\le1-1+3

5x < 20 and
-x\le3

Solve for x to get:

x < 4 and
x\ge -3

The correct choice is C

User ComponentSpace
by
8.5k points

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