Question

WILL FAN AND MEDAL!
A. Given the equation 2(3x − 4) = 5x + 6, solve for the variable. Explain each step and justify your process.
B. Charlie solved a similar equation below. Is Charlie's solution correct? Explain why or why not.
4x − 3 = 2(x − 1)
4x − 3 = 2x + 2
2x − 3 = 2
2x = 6
x =3

Answer 1

A)
2(3x - 4) = 5x + 6
6x - 8 = 5x + 6 Distributive property.
x - 8 = 6 Subtract 5x from both sides.
x = 14 Add 8 to both sides.
Voila!

B) I would probably find the mistake (if there is one) by solving it myself... so I'll do that:
4x - 3 = 2(x + 1)
4x - 3 = 2x + 2 Distributive property (Charlie is right so far)
2x - 3 = 2 Subtract 2x from both sides (Charlie is right so far)
2x = 5 Add three to both sides (Charlie is WRONG here, they multiplied by 3 instead of adding 3)
x = 2.5 Divide both sides by 2.

So... yeah! Hope I helped, and let me know if you need anything else :D

Answer 2

2(3x − 4) = 5x + 6 multiply 2 by the (3x -4)
6x -8 = 5x + 6 to get this
6x-5x = 8 + 6 since we have multiplied, get the x together in The left hand side of the equation and constants together on the other side
x = 14 you will get x afterwards.

Answer 3

Thank you so much! @Sionainn

Answer 4

Anytime, glad I could help :)