### Home > CCA2 > Chapter 3 > Lesson 3.2.2 > Problem3-80

3-80.

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?)

Simplify the equation. What's the GREATEST common factor of these three terms?

Divide by 4000.
x − 2 = 4

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

Solve for x in BOTH equations. Do they yield the same value?

3. 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.

Multiply the equation by the least common denominator to factor out the denominators.

$100\left(\frac{x}{100}\right)+100\left(\frac{3}{100}\right)=100\left(\frac{8}{100}\right)$

Remove the three sets of 100s. They are Giant Ones.

$x + 3 = 8$