Question

Give three numbers that are solutions of the inequality 7x - 33 <11 and three numbers that are not. Justify your responses.

Answer 1

To find solutions to the inequality 7x - 33 < 11, solve for x to get x < 6.2857. Solutions like x=0, x=3, and x=6 satisfy the inequality, while numbers like x=7, x=10, and x=20 do not since after substituting these values into the original inequality, the resulting statement is false.

Step-by-step explanation:

The question asks for solutions to the inequality 7x - 33 < 11. First, we solve for x by adding 33 to both sides of the inequality, yielding 7x < 44, and then dividing both sides by 7, which gives us x < 44/7 or x < 6.2857.

Solutions that satisfy the inequality:

• x = 0 (because 7*0 - 33 < 11)
• x = 3 (because 7*3 - 33 < 11)
• x = 6 (because 7*6 - 33 < 11)

Numbers that do not satisfy the inequality:

• x = 7 (because 7*7 - 33 is not less than 11)
• x = 10 (because 7*10 - 33 is not less than 11)
• x = 20 (because 7*20 - 33 is not less than 11)

To verify whether a number is a solution to the inequality, simply substitute the value into the original inequality and perform the arithmetic to see if the inequality holds true.