Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.B. Megan solved a similar equation below. Is Megan's solution correct? Explain why or why not.
3(2x − 4) = 5x − 1
6x − 12 = 5x − 1
11x − 12 = –1
11x = 11
x = 11

Answers

Answer 1

Answer: A.
$5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \n5x-4=-2 * 3x-2 * 2 \n5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \n11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \n11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \nx=0$

B.
$3(2x-4)=5x-1 \n6x-12=5x-1 \n\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \n11x=11 \n\boxed{x=11} \Leftarrow \hbox{the second mistake}$

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.

The correct solution:
$3(2x-4)=5x-1 \ \ \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \n3 * 2x+3 * (-4)=5x-1 \n 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \nx-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 12 to both sides} \nx=11$

Related Questions

Can someone help me with number 2?
Amelia is standing next to a lighthouse on the edge of a cliff overlooking the ocean. The cliff is 30 meters above sea level, and the lighthouse has a height of 15 meters. There is a man fishing in a boat directly below Amelia who has hooked a fish that is 10 meters below the surface of the water. Use a positive or negative number to represent the location in relation to sea level. Amelia= Top of the Light house= The Boat= The Fish= How many meters is Amelia from the fish?
The sum of the roots of the equation (1/2)x^2-(5/4)x-3=0a.5/2b.2c.1/2
ΔBCD is rotated 80° clockwise about the origin to form ΔKLM. If m∠KLM=30° , what is m∠BCD?m∠BCD=30° m∠BCD=50° m∠BCD=80° m∠BCD=110°
A dice is rolled, then a coin is tossed. What is the probability of getting a 5 then tails?1/121/61/41/35/12

What’s a reflection transformation

Answers

Answer:

A rigid transformation that flips preimage without changing size or shape just the angle over a specific line.

Step-by-step explanation:

"In mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis or plane of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection."

"In geometry, a reflection is a type of rigid transformation in which the preimage is flipped across a line of reflection to create the image. Each point of the image is the same distance from the line as the preimage is, just on the opposite side of the line."

Brainliest please!

Which polynomial is factored completely? a) g^5 - g
b) 4g^3 + 18g^2 + 20g
c) 24g^2 - 6g^4
d) 2g^2 + 5g + 4

Answers

d) 2g² + 5g + 4 is the polynomial that is factored completely.
This is because the terms in the polynomial do not have any common factors.

a) g⁵ - g can be factored into g(g⁴ - 1)
b) 4g³ + 18g² + 20g can be factored into 2g(2g² + 9g + 10)
c) 24g² - 6g⁴ cab be factored into 6g²(4-g²)

Answer: D

Step-by-step explanation:

81 is 56% percent of what

Answers

144.64 is the number whose 56% is 81.

To find what number 81 is 56% of, we can set up the equation:

81 = 0.56x

To solve for x, we divide both sides of the equation by 0.56:

81 / 0.56 = x

x ≈ 144.643

Therefore, 81 is approximately 56 percent of 144.643.

Learn more about percentages here:

brainly.com/question/29306119

#SPJ6

Hey There!

81=0.56x

Divide 81/.56=144.64

x=144.64

So, 81 is 46% of 144.64

Have A Brainly Day!

Tickets to the school play are $5.00 for adults and $3.50 for students. If the total value of all the tickets sold was $2517.50 and 100 more student bought tickets than adults, how many adults amd students bought tickets

Answers

$x-\ adults\ny-\ students\n\n \left \{ {{5x+3.50y=2517.5} \atop {x+100=y}} \right.\n\n5x+3.5(x+100)=2517.5\n\n5x+3.5x+350=2517.5\ \ \ | subtract\ 350\n\n8.5x= 2167,5\ \ \ | divide\ by\ 8.5\n\nx=255\n\ny=355\n\nThere\ were\ 355\ student\ tickets\ and\ 255\ adult\ tickets.$

Given ST Bisects the angle Solve for X
Solve for the m Solve for the m

Answers

Answer:

Step-by-step explanation:

5x + 6 = 3x + 10

2x + 6 = 10

2x = 4

x = 2

m<DST = 3(2) + 10 = 6 + 10 = 16

m<DSE= 5(2) + 6 = 10 + 6 = 16

Mark me brainliest please

A firefighter is attempting to escape a burning building. If the window is of the man's apartment is 18 feet above the ground and the ladder is 25 feet long, what is the angle of elevation?