Solving Equations by Dividing Values

1.7.4 Solving Equations by Dividing Values

1.7.4 • Solving Equations by Dividing Values

Cool Down

The equation $4 (x - 2) = 100$ is a true equation for a particular value of $x$ . Explain why $2 (x - 2) = 50$ is also true for the same value of $x$ .

Compare your answer:

If $4 (x - 2)$ and 100 are equal, then multiplying $4 (x - 2)$ by $\frac{1}{2}$ and multiplying 100 by $\frac{1}{2}$ will give two results that are also equal, so $2 (x - 2) = 50$ must be true.

For questions 2 – 4, use the following situation:

To solve the equation $7.5 = 2.5 d$ , Lin divides each side by $2.5 d$ , and Elena subtracts $2.5 d$ from each side.

Will Lin’s move lead to a solution? Explain your reasoning.

Compare your answer:

Lin's move will not work. Dividing by 2.5d gives 3=1, which is not true. Dividing by the variable we are trying to solve makes us think there is no solution.

Will Elena’s move lead to a solution? Explain your reasoning.

Compare your answer:

Compare your answer: Elena’s move will work. Subtracting 2.5d from both sides gives 5d=0.

What is the solution to the equation?