152k views
0 votes
Hint: You won't flip the sign in every problem. ONLY FUP it when you or by a 9 - 2x < 6x - 15 Solutions You solve and graph these: 3 - 8x -29 Solutions 1x + 2x -7 «6 Solutions 3X-P66 x=4 x=2 free T XCH​

Hint: You won't flip the sign in every problem. ONLY FUP it when you or by a 9 - 2x-example-1
User Rob Lauer
by
8.0k points

1 Answer

2 votes

You only flip the inequality sign when you multiply or divide both sides by a negative number.

================================================

Problem 1


3 - 8x \ge -29\\\\-8x \ge -29-3\\\\-8x \ge -32\\\\x \le (-32)/(-8) \ \text{ inequality sign flip}\\\\x \le 4

The inequality sign flip happens because we divided both sides by -8.

The graph will have a closed circle at 4 with shading to the left.

Three solutions are x = 0, x = 1, x = 2. You can pick any three numbers you want as long as they are 4 or smaller.

================================================

Problem 2


1x+2x-7 < 6\\\\3x-7 < 6\\\\3x < 6+7\\\\3x < 13\\\\x < (13)/(3)\\\\x < 4 (1)/(3)

The graph will have an open circle at 13/3 = 4&1/3 = 4.333 approx. The shading is to the left. No inequality sign flip happens because we divided both sides by a positive number.

Your choice of three solutions is correct. You can pick anything smaller than 4.3333

================================================

Problem 3


9-2x \le 6x-15\\\\-2x-6x \le -15-9\\\\-8x \le -24\\\\x \ge (-24)/(-8) \ \text{ inequality sign flip}\\\\x \ge 3

The solution set is any value 3 or larger. Three solutions are x = 5, x = 6 and x = 7.

The graph has a closed circle at 3 on the number line. The shading is to the right.

User Matt Gartman
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.