### Home > CC4 > Chapter 3 > Lesson 3.3.1 > Problem3-114

3-114.

Now David wants to solve the equation $4000x−8000=16,000$. Homework Help ✎

1. What easier equation could he solve instead that would give him the same solution? (In other words, what equivalent equation has easier numbers to work with?)

• Divide both sides of the equation by a common factor.

• $\frac{4000\textit{x}-8000}{4000} = \frac{16000}{4000}$

x − 2 = 4

1. Justify that your equation in part (a) is equivalent to $4000x−8000=16,000$ by showing that they have the same solution.

• Solve both equations for x.
x − 2 = 4 4000x − 8000 = 16000
x = 6 4000x = 24000
x = 6

The equations have the same answer.

1. David’s last equation to solve is $\frac { x } { 100 } + \frac { 3 } { 100 } = \frac { 8 } { 100 }$. Write and solve an equivalent equation with easier numbers that would give him the same answer.

• Multiple both sides of the equation by 100.