Question

Find all real numbers x such that

\[4x + 2 \ge 14\]

and

\[-21x + 1 > 22\]


I am not looking for someone to give me the answer here, I am looking for someone to check my work to make sure I'm doing it right as I want to catch any mistakes now before I submit the assignment for grading. Posting the answers here will not get a medal!

Answer 1

\[4x + 2 \ge 14\]

is equal to

\[x \ge 4\]

Answer 2

-21x + 1 > 22
-1 -1

-21x > 21
/-21 /-21

x < -1

Answer 3

How do you get x greater than or equal to 4?

Answer 4

What u have done for the second part is right:) Pls chck the first part

Answer 5

There's a mistake in second part too

Answer 6

oops sorry my bad/. yup u r @Abdul_shabeer

Answer 7

basically when I redid my work for the first part I got...

\[x \ge 3\]

Answer 8

That's right

Answer 9

Okay and looking at the work for the 2nd one, I'm not really sure where I went wrong.

Answer 10

Everything is fine except the final line

Answer 11

21 / -21 = -1 correct?

Answer 12

Okay, so when I was taught this, I was told that if your graphing these equations on a number line and you have to divide by a negative, the inequality sign flips to the opposite sign. Is that wrong?

Answer 13

@abdul_shabeer If your graphing these equations on a number line and you have to divide by a negative, the inequality sign flips to the opposite sign. Is that wrong?

Answer 14

If x is less than -1, then it doesn't satisfy the inequality

Answer 15

So there would be no real numbers in this set?

Answer 16

Wait, nevermind. We can still add the numbers from \[x \ge 3\]

So it would be an open dot on 3 with the shading to the right?

Answer 17

@ajprincess did I do it right?

Answer 18

Well I thnk u r right. cos
real numbers include all positive negative integers , decimal numbers and all

Answer 19

\(x\ge3\) the dot also will be a shaded one

Answer 20

I mean ur second part too is right