Answer:
- Subtraction (addition) property of inequality
- Addition property of inequality
- Division property of inequality
Explanation:
You want the reasons for each of the final three steps in the solution of the inequality 7x +16 < -5(5 -5x).
Steps
2. 7x +16 < -20 +25x . . . . . . . given step 2
3. 16 < -20 +18x . . . . . Subtraction property of inequality
- 7x was subtracted from both sides
4. 36 < 18x . . . . . . . . . Addition property of inequality
- 20 was added to both sides
5. 2 < x . . . . . . . . . . . . Division property of inequality
- both sides were divided by 18
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Additional comment
Subtraction of 7x is the same as adding -7x, so you can say the reason for step 3 is either of "subtraction property" or "addition property" The same would be true of step 4.
To figure this out, you compare the inequality on each line with the one before, and determine what was changed. If the same thing is done to both sides of the inequality (addition, subtraction, multiplication, division), the reason is the corresponding property of inequality.
The multiplication and division properties of inequality tell you to reverse the comparison symbol when the factor used is negative. Here, the factor is 18, a positive number, so the inequality symbol remains untouched.
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