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Example 2.30 from Prealgebra, 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
Write an equation modeled by the envelopes and counters, and then solve the equation:
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
| On the left, write for the contents of the envelope, add the counters, so we have . | |
| On the right, there are counters. | |
| The two sides are equal. | |
| Solve the equation by subtracting counters from each side. |
We can see that there is one counter in the envelope. This can be shown algebraically as:
Substitute for in the equation to check.
Since makes the statement true, we know that is indeed a solution.
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Write the equation modeled by the envelopes and counters, and then solve the equation:
How did it go?