Working Backwards: Make Equations With A Given Solution

Build equations with a chosen solution by doing the same thing to both sides, and use one equation to find related values without solving.

5 micro-lessons

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Build Up from the Answer

Start from y = 5 and do the same thing to both sides.

Start from the solution and do the same operation to both sides, one step at a time. Every new equation has the same solution.

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Example 13, and using 4k + 1 = 13 without solving.

Problem 1 (Example 13, p. 180). Give a real-life situation for 100x + 75 = 250.

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Same operation, both sides, same solution.

Building equations (Textbook pp. 179–180)

Start from

x = value

Add, subtract, multiply or divide both sides by the same number (never divide by zero), as many times as you like.

Every equation in the chain has the same solution.

To use a given equation like

4 k + 1 = 13

, look for it, or a multiple of it, inside the new expression.

Write your own equations with a chosen solution.

Make equations with a given solution

Figure it Out, Textbook p. 181, Q1 and p. 188, Q13.

Use the chain idea: start from the solution and do the same thing to both sides.

Evaluate expressions from a given equation.

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Given 4k + 1 = 13, what is 8k + 2?