5(n + 6) = 2(n-3) +4

a. 5n + 6 = 2n +1

b. 5n + 30 = 2n - 2

c. 5n +6=2n - 2

d. in + 30 = 2n +1

The most obvious one i can think of would be

x = 13

Step-by-step explanation:

x + 8 = 21

x + 8-8 = 21-8

x = 13

Question:

Let .

Which equation is equivalent to in terms of p ?

or

Step-by-step explanation:

Given

.

Required

Find the equation equivalent to

To get the equation equivalent to the given expression, we simply simplify and solve in terms of p

Factorize expression on the right hand side

Substitute for p

becomes

Hence, equation is equivalent to

Solving further to get the value of p

Subtract 9p from both sides

Rearrange

Factorize

p - 3 = 0 or p - 6 = 0

p = 3 or p = 6

Question 1:

For this case we must rewrite the following equation:

If we add 3x to both sides of the equation we have:

Thus, we have that an equivalent expression is option C.

Option C

Question 2:

For this case we must solve the following equation:

Subtracting 5 from both sides of the equation we have:

Dividing between -5 on both sides of the equation we have:

Option B

D

Step-by-step explanation:

given

(5x - 2)² + 35x - 14 = - 12 ← factor out 7 from 35x - 14

(5x - 2)² + 7(5x - 2) = - 12 ( add 12 to both sides )

(5x - 2)² + 7(x - 2) + 12 = 0 ← substitute m = 5x - 2, hence

m² + 7m + 12 = 0 → D

m² - 13m + 42 = 0

Step-by-step explanation:

Given m = x²

Then original equation

( x² - 5 )² - 3x² + 15 = -2

Now replace x² by m

( m - 5 )² - 3m + 15 = -2

Now considering ( m - 5 )² , we can open or expand the expression and later simplify. Therefore

( m - 5 )² = m² -10m + 25

Now put this in the above expression and simplify.

( m- 5 )² - 3m + 15 = -2 ,now becomes

(m² - 10m + 25) - 3m + 15 = -2

m² - 10m -3m + 25 + 15 + 2 = 0

m² - 13m + 42 = 0

Step-by-step explanation:

We can go simplify the equation by simplifying the first polynomial:

Then, we can substitute that in the original equation:

Now, we can substitute m for every x^2.

Knowing that x^4 = x^2 * x^2, we can write this as m^2:

b. 5n + 30 = 2n - 2

Step-by-step explanation:

The distributive property requires the outside factor be applied to every term inside parentheses. After eliminating parentheses using the distributive property, terms can be collected on the right.

5(n +6) = 2(n -3) +4

5n +5·6 = 2n +2(-3) +4

5n + 30 = 2n -6 +4

5n + 30 = 2n - 2 . . . . . matches choice B

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