1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
natka813 [3]
3 years ago
14

Solve: -8(x - 3) + 5x < 9(x + 12) This is Algebra 1

Mathematics
2 answers:
yaroslaw [1]3 years ago
7 0

Answer:

The answer is x > -7

Step-by-step explanation:

The starting out equation is:

-8(x - 3) + 5x < 9(x + 12)

Once you've got your equation down, you have to remove the parentheses by doing <u>distributive</u><u> </u><u>property</u><u>,</u> and multiplying the -8 by x and -3, [-8(x-3)] and the 9 by x and 12, [9(x + 12)]

Once you do that, you have something like this:

-8x + 24 + 5x < 9x + 108

Then you have to add like terms. That means adding -8x to the positive 5x, and only that since thats the only possible way.

-3x + 24 < 9x + 108

When that's over, you have to move the variable(in my case, 9x) to the left-hand side and change its sign:

-3x -9x + 24 < 108

You see that instead of positive 9x, like it was, it's now negative 9x since we changed its location.

And now do the same to the constant (in my case, 24) to the right-hand side. make sure to reverse its sign aswell, so now it's a negative 24. Now it looks a bit like this:

-3x -9x < 108 -24

Collect like terms (subtracting -9x by -3x, subtracting 108 by -24)

-12x < 84

Now that we isolated the variable, we have to divide it by -12.

KEEP IN MIND!!

When doing work like this, at some point you have to divide the variable by itself, and same thing to the other side. When the variable is a positive number and you're dividing by a positive number, DONT REVERSE THE GREATER/LESS (whatever you have) SIGN!!

When you are dividing by a negative number,

REVERSE THE SIGN!!

I always forgot this and got it wrong back then!!

Back to the lesson, itll look like this when dividing

-12x < 84

------ ------

-12x -12x

Once you divide it, you'll get this

x > -7

I hope this helped!

Flauer [41]3 years ago
4 0

Answer:

x>−7

Step-by-step explanation:

left side:

-8(x-3)+5x

distribute -8 into (x-3)

-8x+24+5x

combine like terms

-3x+24

right side:

9(x+12)

distribute 9 into (x+12)

9x+108

-3x+24<9x+108

Subtract 24 on both sides

-3x< 9x+108-24

combine like terms

-3x<9x+84

Subtract 9x on both sides

-3x-9x<+84

combine like terms again

-12x<84

Multiply both sides by -1 (reverse the inequality)

(-12x)(-1)>84(-1)

12x>-84

divide both sides with 12

\frac{12x}{12}>\frac{-84}{12}

x>−7

hope this helps

You might be interested in
Decrease the number 14.4 by 0.2 of it.
adell [148]

The result of the decrease of the number 14.4 by 0.2 of it is of 14.2.

<h3>What does it mean to decrease a number a by b of it?</h3>

The equivalent operation is the subtraction of a by b.

In this problem, we want to decrease the number 14.4 by 0.2 of it, hence the operation is:

14.4 - 0.2 = 14.2.

More can be learned about subtraction operations at brainly.com/question/4721701

#SPJ1

3 0
2 years ago
Write a conditional statement for a following Venn diagram
Amanda [17]

The image shows that all integers are rational numbers, but there are rational numbers that are not integers.

The formal statement would be

\mathbb{Z}\subset \mahtbb{Q}

6 0
3 years ago
Two lines have the following equations
Mashcka [7]

Answer:

(4,-3)

Step-by-step explanation:

Easiest way to do this without any advanced methods is to use the answer choices to your advantage.  

For a.) we have (1,1) meaning x = 1 and y = 1 if we get a 7 for the first equation and a -2 for the second equation then that is the correct answer.

Let x=1, y =1:

4(1)+3(1)=4+3=7  Correct so far.

1+2(1)=1+2=3      Incorrect since we should have got a -2 if this was the solution


Let (0,-1) x = 0, y = -1:

4(0) + 3(-1) = 0 -3 = - 3 Incorrect so we can stop there next answer choice.


Let (4,-3) x = 4 y = -3:

4(4)+3(-3)=16-9=7   Correct so far.

4+2(-3)=4-6=-2      Both are correct!

Therefore the solution (where the lines intersect) is (4,-3).


4 0
2 years ago
The list of all factors for 21 is 1, 3, 7, and 21.<br><br> True or False<br> plz i need help
antiseptic1488 [7]

Answer:

true

Step-by-step explanation:

hope you have a wonderful new year

3 0
3 years ago
Read 2 more answers
Mr Amadi left his house by 6:30am and returned by 8:05pm. how long was he away from home​
SpyIntel [72]

Answer:14 hrs and 25 mins

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • PLZ HELP :) 10 PTS
    13·1 answer
  • Find the difference between 24 1/8 minus 6 3/4
    12·2 answers
  • Wendy's older brother is buying a car.He can make 24 payments of $95 or 30 payments of $80 each. Which costs less?How much less.
    11·2 answers
  • The ratio of adults to children in a movie theater is 7:2. If there are 26 children in the theater, how many adults are there?
    13·1 answer
  • X^2+20=2x what are the values of x?
    9·2 answers
  • Area of the base, B = 42 square meters<br><br> and height = 3 meters
    5·1 answer
  • David, Chen, and Leslie raised money for the school in a walk-a-thon. Altogether they made $46. Leslie made $10. Chen made twice
    12·1 answer
  • 2 people can paint a fence in one hour, how long would it take 10 people, give your answer in minutes
    8·2 answers
  • Pls help i am stuck on this
    5·1 answer
  • PLEASE HELP I HAVE 4 MINUTES TO DO THIS WHATS 6+6​
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!