(2x+1)^{2} -(x+2)^{2} =|(x+2016)(x^{2} -1)

Need help with these

liraira [26]

1. 4(2+3c) = 56

c = 4

3. -29 = 5(2a-1)+2a

a = -2

5 . 7p-(3p+4) = -2(2p-1)+10

p=2

7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)

x=4

Step-by-step explanation:

1. 4(2+3c) = 56

$4(2+3c) = 56\\8+12c = 56$

Subtracting 8 from both sides

$8-8+12c = 56-8\\12c = 48$

Dividing both sides by 12

$\frac{12c}{12} = \frac{48}{12}\\c = 4$

Checking:

$4[2+3(4)] = 56\\4(2+12) = 56\\4(14) = 56\\56 = 56$

3. -29 = 5(2a-1)+2a

Simplifying

$-29 = 10a-5+2a\\-29 = 12a-5$

Adding 5 on both sides

$-29+5 = 12a - 5+5\\-24 = 12a$

Dividing both sides by 12

$\frac{12a}{12} = \frac{-24}{12}\\a = -2$

Checking:

$-29 = 5(2a-1)+2a\\-29 = 5[2(-2)-1]+2(-2)\\-29 = 5(-4-1) -4\\-29 = 5(-5) -4\\-29 = -25-4\\-29 = -29$

5 . 7p-(3p+4) = -2(2p-1)+10

Simplifying

$7p-3p-4 = -4p+2+10\\4p-4 = -4p+12$

Adding 4 on both sides

$4p-4+4 = -4p+12+4\\4p = -4p+16$

Adding 4p on both sides

$4p+4p = -4p+4p+16\\8p = 16$

Dividing both sides by 8

$\frac{8p}{8} = \frac{16}{8}\\p = 2$

Checking:

$7p-(3p+4) = -2(2p-1)+10\\7(2)-[3(2)+4] = -2[2(2)-1] +10\\14 - (6+4) = -2 (4-1) +10\\14 - 10 = -2(3) +10\\4 = -6+10\\4=4$

7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)

Simplifying

$\frac{1}{2} (-4+6x) = \frac{1}{3}x+\frac{2}{3}(x+9)\\\frac{-4}{2}+\frac{6x}{2} = \frac{x}{3} +\frac{2x}{3} + \frac{18}{3}\\-2+3x = \frac{x+2x+18}{3}\\-2+3x = \frac{3x+18}{3}\\3(-2+3x) = 3x+18\\-6+9x = 3x+18$

Adding 6 on both sides

$-6+6+9x = 3x+18+6\\9x = 3x+24$

Subtracting 3x from both sides

$9x-3x = 3x-3x+24\\6x = 24$

Dividing both sides by 6

$\frac{6x}{6} = \frac{24}{6}\\x = 4$

Checking:

$\frac{1}{2} [-4+6(4)] = \frac{1}{3}(4)+\frac{2}{3}(4+9)\\\frac{1}{2}(-4+24) = \frac{4}{3}+\frac{2}{3}(13)\\\frac{1}{2}(20) = \frac{4}{3} +\frac{26}{3}\\15 = \frac{4+26}{3}\\15 = \frac{30}{3}\\15=15$

Keywords: Linear equations

Learn more about linear equations at:

#LearnwithBrainly

6 0

3 years ago

Jane has 5.8 pints of juice.

Juliette [100K]

Answer:

144 cups-14 pints

Step-by-step explanation:

7 0

3 years ago

Do people improve their timing on an online crossword puzzle with an additional attempt? Twenty people were timed to complete a

oksano4ka [1.4K]

Answer:

Step-by-step explanation:

Yes there should be an improvment. they should remember some of the answers to the puzzle they did the first time, so the second time, it would be faster and easier.

3 0

4 years ago

Overige

MAVERICK [17]

Answer:

the answae is D THEN C THE. 1

3 0

3 years ago

I am studying for a discrete math final and I do not understand the provided solution. Specifically, how to rationalize "C(12,10

vovangra [49]

Answer:

Step-by-step explanation:

Given is an equation in three variables

$x_1+x_2+x_3 =10$ where the three variables are non negative integers.

Since sum =10, and each integer has minimum value 1, we find that each variable can take values as 1,2,...8 only

If first variable is 1, the other two can be 1,8 or 2,7 or... 8,1 ... 8 ways

If first variable is 2, ... the other two can be 1,7 or 2,6 or..7,1 ... 7 ways

This will go up to first variable =8

Thus we have total number of solutions as

$8+7+6+5+...+1\\=36$

Thus possible solutions are 36

5 0

4 years ago