Could you please help?
What are the solutions of the compound inequality? 2x - 2 < - 12 or 2x+3 > 7
Is this one x < - 5 or x> 2
2x -1/3 +3 <= -4. Or 8x-2/2 -1 >= 6.
This one is 2x-1 divided by 3 plus 3 is less than or equal to - 4 or 8x -2 divided by 2 minus one is greater or equal to six just incase you can't read my typing,
Thank you.
2x-2 < -12
2x < -10
x < -5
2x+3 > 7
2x > 4
x > 2
So, x < -5 or x > 2
Work the other in like wise. Just clear the fractions first to make things easier.
Oh, inequality problems, my favorite! Let's solve them with a touch of humor, shall we?
For the compound inequality 2x - 2 < -12 or 2x + 3 > 7, you're correct! The solutions are x < -5 or x > 2. It's like saying, "Hey x, don't you dare get close to -5 or play around with anything greater than 2!"
Now, onto the second one, where things get a bit more tricky. We have 2x - 1/3 + 3 <= -4 or 8x - 2/2 - 1 >= 6. Well, let's see what we've got here.
For the first part, 2x - 1/3 + 3 <= -4, it's like saying, "Hey x, be less than or equal to -4, but first, let me give you a little math puzzle to solve!" But worry not, I got your back.
Start by subtracting 3 from both sides: 2x - 1/3 <= -7. Ah, we're almost there! Now, to get rid of that pesky fraction, multiply everything by 3: 6x - 1 <= -21.
Finally, add 1 to both sides: 6x <= -20. And guess what? Divide by 6 on both sides and you've got x <= -20/6, which simplifies to x <= -10/3. Ta-da!
Now, let's tackle the second part: 8x - 2/2 - 1 >= 6. Here we go again! It's like telling x, "Listen buddy, you better be greater than or equal to 6, but only after solving this little mathematical riddle!"
First, let's simplify the fraction: 8x - 1 - 1 >= 6. See that sneaky 2/2 transformed into a plain old 1? That's the magic of math!
Next, combine like terms: 8x - 2 >= 6. We're making progress! Now, add 2 to both sides: 8x >= 8.
Fantastic! Just divide by 8 on both sides and you're left with x >= 1. Mission accomplished!
I hope that humorously clears things up for you. Just remember, with inequalities, it's all about setting boundaries for x and watching it dance within those limits. Good luck!
Sure, I'd be happy to help!
For the first compound inequality, let's solve each inequality separately and then combine the solutions:
1. Solve 2x - 2 < -12:
Add 2 to both sides of the inequality:
2x - 2 + 2 < -12 + 2
Simplify:
2x < -10
Divide both sides by 2 (since the coefficient of x is 2):
x < -5
2. Solve 2x + 3 > 7:
Subtract 3 from both sides of the inequality:
2x + 3 - 3 > 7 - 3
Simplify:
2x > 4
Divide both sides by 2 (since the coefficient of x is 2):
x > 2
The solutions to the compound inequality are x < -5 or x > 2.
Now, let's solve the second compound inequality:
1. Solve 2x - 1/3 + 3 <= -4:
Combine like terms on the left side:
2x + 2 + 3/3 <= -4
Simplify the fraction:
2x + 2 + 1 <= -4
Combine like terms:
2x + 3 <= -4
Subtract 3 from both sides of the inequality:
2x + 3 - 3 <= -4 - 3
Simplify:
2x <= -7
Divide both sides by 2 (since the coefficient of x is 2):
x <= -7/2
2. Solve 8x - 2/2 - 1 >= 6:
Combine like terms on the left side:
8x + 1 - 1 >= 6
Combine like terms:
8x >= 6
Divide both sides by 8 (since the coefficient of x is 8):
x >= 3/4
The solutions to the second compound inequality are x <= -7/2 or x >= 3/4.
I hope this helps! Let me know if you have any other questions.
To find the solutions of a compound inequality, you need to solve each inequality separately and then combine the solutions.
For the first compound inequality, we have:
2x - 2 < -12 or 2x + 3 > 7
To solve the first inequality, 2x - 2 < -12:
Adding 2 to both sides, we get:
2x - 2 + 2 < -12 + 2
2x < -10
Dividing both sides by 2, we get:
x < -5
To solve the second inequality, 2x + 3 > 7:
Subtracting 3 from both sides, we get:
2x + 3 - 3 > 7 - 3
2x > 4
Dividing both sides by 2, we get:
x > 2
Therefore, the solution to the compound inequality is x < -5 or x > 2.
For the second compound inequality, we have:
2x - (1/3) + 3 <= -4 or (8x - 2)/2 - 1 >= 6
To solve the first inequality, 2x - (1/3) + 3 <= -4:
Subtracting 3 from both sides, we get:
2x - (1/3) + 3 - 3 <= -4 - 3
2x - (1/3) <= -7
Multiplying both sides by 3, we get:
6x - 1 <= -21
Adding 1 to both sides, we get:
6x - 1 + 1 <= -21 + 1
6x <= -20
Dividing both sides by 6, we get:
x <= -20/6 = -10/3 = -3.33 (rounded to two decimal places)
To solve the second inequality, (8x - 2)/2 - 1 >= 6:
Adding 1 to both sides, we get:
(8x - 2)/2 - 1 + 1 >= 6 + 1
(8x - 2)/2 >= 7
Multiplying both sides by 2, we get:
8x - 2 >= 14
Adding 2 to both sides, we get:
8x - 2 + 2 >= 14 + 2
8x >= 16
Dividing both sides by 8, we get:
x >= 2
Therefore, the solution to the second compound inequality is x <= -3.33 or x >= 2.
I hope this explanation helps! Let me know if you have any further questions.