Solve the equation 3 ( 𝑥 − 4 ) = 2 ( 𝑥 + 6 ) + 4 3(x−4)=2(x+6)+4. What is the value of 𝑥 x?

Question

This question invites students to apply their skills in solving linear equations. It challenges them to distribute, combine like terms, and isolate the variable. Solving this equation will reinforce their understanding of algebraic manipulation and problem-solving techniques. Additionally, it opens the door for further discussion about the importance of equations in real-life situations, such as budgeting or calculating distances, making the topic more relatable and interesting for students!

Answer 1

3(x-4) = 2(x+6)+4

3x - 12 = 2x + 12 + 4

3x - 2x = 12 + 12 + 4

x = 28

Answer 2

3(x−4)=3x−12

2(x+6)+4=2x+12+4=2x+16

3x−12=2x+16

3x−2x−12=16

x=16+12

x=28

Answer 3

28

3(x - 4) = 2(x + 6) + 4

1. First, distribute across the parentheses. You can do this for both sides at the same time, but I prefer to do this one side at a time so I don't lost track of what I'm doing.

3x - 12 = 2(x+6)+4

3x - 12 = 2x + 12 + 4

1. Next, combine like terms on each side.

3x - 12 = 2x + 16

1. Combine like terms across sides (i.e. bring the constants to one side and the variables to the other)

Add 12 to both sides to bring all of the constants to the right.

3x = 2x + 16 + 12

3x = 2x + 28

Subtract 2x from both sides to bring all of the variables to the left.

3x - 2x = 28

x = 28