Home > MC2 > Chapter 6 > Lesson 6.2.6 > Problem6-128

6-128.

Some steps in solving an equation are more efficient than others. Complete parts (a) through (d) to determine the most efficient first step to solve the equation $34 = 5x-21$.

1. If both sides of the equation were divided by $5$, then the equation would be $\frac { 34 } { 5 } = x - \frac { 21 } { 5 }$. Does this make the problem simpler? Why or why not?

Fractional coefficients are more complex and can be harder to deal with than whole number coefficients.

2. If we subtract $34$ from both sides, the equation becomes $0 = 5x-55$. Does this make the equation simpler to solve? Why or why not?

All terms are on one side of the equation.

3. If we add $21$ to both sides, the equation becomes $55 = 5x$. Does this suggestion make this a problem you can solve more easily? Why or why not?

The variable $x$ has been isolated on one side of the equation. What would you do next to solve the equation?
Is this one less step than you would take for the other first steps from parts (a) and (b)?

4. All three suggestions are legal moves, but which method will lead to the most efficient solution? Why?

Part (c) is the most efficient method. Can you see why?
Try using each method to see which is the quickest with the least steps to solve the equation.