Question

unit activity: foundations of geometry
question 1
complete the missing reasons for the proof.
given: 4(x - 2) = 6x + 18
prove: x = -13
statements | reasons

1. 4(x - 2) = 6x + 18 | given
2. 4x - 8 = 6x + 18 | distributive property
3. -2x - 8 = 18 |
4. -2x = 26 | addition property of equality
5. x = -13 |

options:
○ 3. addition property of equality; 5. multiplication property of equality
○ 3. subtraction property of equality; 5. division property of equality
○ 3. subtraction property of equality; 5. multiplication property of equality
○ 3. addition property of equality; 5. division property of equality

Explanation:

Step1: Analyze Step 3 transition

To get from $4x - 8 = 6x + 18$ to $-2x - 8 = 18$, subtract $6x$ from both sides. This uses the subtraction property of equality (subtracting the same value from both sides preserves equality).

Step2: Analyze Step 5 transition

To get from $-2x = 26$ to $x = -13$, divide both sides by $-2$. This uses the division property of equality (dividing both sides by the same non-zero value preserves equality).

Answer:

1. subtraction property of equality; 5. division property of equality