Solving Equations in One Unknown
The steps needed to solve almost any equation in one unknown can be described with the pneumonic device.
| Step 1 | D | Distribute. |
| Step 2 | C | Collect like terms on the each side of the equation. |
| Step 3 | 0 | Undo all additions and subtractions on each side of the equation. |
| Step 4 | 1 | Undo all multiplications and divisions. |
Directions: Please solve for the unknown in the following equation.
Using the DC01 method we have the following.
Directions: Please solve for the unknown in the following equations. If there is no solution, please indicate so by stating "null set".
Directions: Please answer the following word problems.
1. Twice a number decreased by four is four times the number increased by five. What is the number?
2. The formula for the area of a square is A=s2, where A is the area and s is the side of the square. If the area of a square is 48, what is the length of the side of the square?
3. The formula for the area of a trapezoid is A=1/2*h*(b1+b2), where A is the area, h is the height and b1 & b2 are the bases. When the height is 10 and one base is twice the length of the other base, the area of a trapezoid is 75. What are the length of the bases of the trapezoid?
Directions: Please write 1-2 paragraphs that throughly address the following.
1. Consider the following two statements.
A. |
B. |
If you were asked to solve the above equations for the unknown, which problem do you think would be harder? Why or why not? Would you say the same thing, if you were using a calculator? Why or why not? Be specific. Be sure to mention the number of steps and the types of steps involved.
2. If step 3 described above is to "Undo all additions and subtractions on each side of the equation", why do we use "0" as the pnemonic device for this step?
3. Similarly to question 2, If step 3 described above is to and "1" do designate steps three and four respectively? "Undo all multiplications and divisions on each side of the equation", why do we use "1" as the pnemonic device for this step?