For clarity, here is the condition in fraction notation:

$\frac{x+\mathrm{10}}{-5}>3$

The inequality properties allow us to multiply -5 to both sides, but we need to flip the operator to the less-than sign (<).

Then this equation becomes:

x + 10 < 15

Next, we can add -10 to both sides to reach the conclusion.

Quiz (1 point)

• a / b = a ⋅ (1 / b)
• -5 < 0
• 3 ⋅ (-5) = -15
• (1 / (-5)) ⋅ (-5) = 1
• (-15) + (-10) = -25
• 10 + (-10) = 0

• if the following are true:

  • a > b
  • a = c

  then c > b

• if the following are true:

  • a > b
  • c < 0

  then a ⋅ c < b ⋅ c

• if b ⋅ c = d, then (a ⋅ b) ⋅ c = a ⋅ d

• if the following are true:

  • a < b
  • a = x
  • b = y

  then x < y

• if a ⋅ 1 < b, then a < b

• if a < b, then a + c < b + c

• if b + c = d, then (a + b) + c = a + d

• if the following are true:

  • a < b
  • a = x
  • b = y

  then x < y

• if a + 0 < b, then a < b

Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.

Step	Claim	Reason (optional)	Error Message (if any)
1
2
3
4
5
6
7
8
9
10

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