Question

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​

Answer 1

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

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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.

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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

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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.