2.5.1 Writing and Evaluating New Equations

Algebra 12.5.1 Writing and Evaluating New Equations

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Activity

Look at the following equation: $50 + 1 = 51$ .

Perform each of the following operations and answer these questions: What does each resulting equation look like? Is it still a true equation?

Add 12 to each side of the equation.

Compare your answer:

$50 + 1 + 12 = 51 + 12$ , or $63 = 63$ (or equivalent). Yes, it is still a true equation.

Add $10 + 2$ to the left side of the equation and 12 to the right side.

Compare your answer:

$50 + 1 + 10 + 2 = 51 + 12$ , or $63 = 63$ (or equivalent). Yes, it is still a true equation.

Add the equation $4 + 3 = 7$ to the equation $50 + 1 = 51$ .

Compare your answer:

$50 + 1 + 4 + 3 = 51 + 7$ , or $58 = 58$ (or equivalent). Yes, it is still a true equation.

Write a new equation that, when added to $50 + 1 = 51$ , gives a sum that is also a true equation.

Compare your answer:

Your answer may vary, but here are some samples.

$8 + 2 = 10$ . Added to the original equation gives: $50 + 1 + 8 + 2 = 51 + 10$ , or $51 + 10 = 61$ , or $61 = 61$ .
$a + a = 2 a$ . Added to the original equation gives: $50 + 1 + a + a = 51 + 2 a$ , or $51 + 2 a = 51 + 2 a$ .

5. Write a new equation that, when added to $50 + 1 = 51$ , gives a sum that is a false equation.

Compare your answer:

Your answer may vary, but here are some samples

$3 + 2 = 7$ . Added to the original equation gives: $50 + 1 + 3 + 2 = 51 + 7$ , or $56 = 58$ , which is false.
$a + 2 = a$ . Added to the original equation gives: $50 + 1 + a + 2 = 51 + a$ , or $53 + a = 51 + a$ , which is false.

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
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- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
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- Section URL: https://openstax.org/books/algebra-1/pages/2-5-1-writing-and-evaluating-new-equations

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