Question

Drag each tile to the correct location on the algebraic problem. Not all tiles will be used,
Fill in the missing steps and justifications used to solve the given equation.
Subtraction property of equality
61 - 7 - 12 = 12 + 7
Simplification
61 - 7 + 7 = 12 +7
Addition property of equality
Multiplication property of equality
1 = 114 = =
41-7 = -20 +12
1. Given
43 - 7 + 20 = -21 + 12 + 23
2. Addition property of equality
6.3 - 7 = 12
3.
4.
63 = 19
5. Simplification
6. Division property of equality
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Answer 1

Answer/Step-by-step explanation:

4x - 7 = -2x + 12 (Given)

Add 2x to both sides

4x - 7 + 2x = -2x + 12 + 2x (Addition property of equality)

6x - 7 = 12 (Simplication)

Add 7 to both sides

6x - 7 + 7 = 12 + 7 (Addition property of equality)

6x = 19 (Simplification)

Divide both sides by 6

$\frac{6x}{6} = \frac{19}{6}$ (Division property of equality)

$x = \frac{19}{6}$

Answer 2

The correct justification, provides the right reasons for the given

mathematical operation.

Responses:

3. Simplification

6·x - 7 + 7 = 12 + 7  ${}$             4. Addition property of equality

How are the correct justifications found?

The two column solution is presented as follows;

Step ${}$                                               Justification

4·x - 7 = -2·x + 12  ${}$                       1. Gives

4·x - 7 + 2·x = -2·x + 12 + 2·x ${}$     2. Addition property of equality

6·x - 7 = 12  ${}$                                 3. Simplification

6·x - 7 + 7 = 12 + 7 ${}$                      4. Addition property of equality

6·x = 19 ${}$                                       5. Simplification

$\dfrac{6 \cdot x}{6} = \dfrac{19}{6}$                           ${}$           6. Division property of equality

Learn more about the properties of equality here:

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