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.
19
6
Subtraction property of equality
6x7 - 12 = 12 + 7 Addition property of equality
x=
Simplification
6x7+7= 12 + 7
4x7= -2x + 12
4x7+2x = -2x + 12 + 2x
6x - 7 = 12
6x = 19
Multiplication property of equality
1. Given
2. Addition property of equality
3.
x = 114
4.
5. Simplification
6. Division property of equality
7. Simplification

Answer 1

To solve the equation 6x7 - 12 = 12 + 7, apply the Addition Property of Equality to combine like terms and simplify both sides of the equation. Then, use the Subtraction Property of Equality to isolate the variable x. Finally, solve for x by applying the Multiplication Property of Equality to both sides of the equation.

Step-by-step explanation:

Given equation: 6x7 - 12 = 12 + 7

Apply the Addition Property of Equality to add 12 + 7, which gives 6x7 - 12 + 12 + 7 = 12 + 7 + 12.

Simplify both sides of the equation to get the equation 6x7 + 7 = 12 + 7.

Combine like terms on both sides of the equation to simplify further, leading to 42 + 7 = 12 + 7.

Simplify both sides of the equation to get the equation 49 = 19.

Using the Subtraction Property of Equality, subtracting 7 from both sides of the equation gives 6x = 19 - 7.

Simplify both sides of the equation to get the equation 6x = 12.

Finally, apply the Multiplication Property of Equality to divide both sides of the equation by 6, which gives the solution x = 2.

Answer 2

Based on the given algebraic problem and the provided tiles, let's match the tiles to the correct steps and justifications:

1. Given

2. Addition property of equality

- Tile: 6x7+7= 12 + 7

- Justification: This step uses the addition property of equality, which allows adding the same value to both sides of an equation.

3. Simplification

- Tile: 4x7= -2x + 12

- Justification: This step simplifies the equation by combining like terms on both sides.

4.

5. Simplification

- Tile: 6x - 7 = 12

- Justification: This step simplifies the equation by combining like terms on the left side.

6. Division property of equality

- Tile: 6x = 19

- Justification: This step uses the division property of equality, which allows dividing both sides of an equation by the same non-zero value.

7. Simplification

- Tile: x = 114

- Justification: This step simplifies the equation by solving for the variable x.

The missing steps and justifications are as follows:

4. Subtraction property of equality

- Tile: 4x7+2x = -2x + 12 + 2x

- Justification: This step uses the subtraction property of equality, which allows subtracting the same value from both sides of an equation.

By including these missing steps and justifications, the solution to the given algebraic problem will be complete.