Question

Step 3: 2x > 10 Step 4: x > 5 What property justifies the work between step 3 and step 4? A. division property of inequality B. inverse property of multiplication C. subtraction property of inequality D. transitive property of inequality

Answer 1

A. Division property of inequality.

Explanation:

Let be
`2\cdot x > 10`, we proceed to show the appropriate procedure to step 4:

1)
`2\cdot x >10` Given

2)
`x > 5` Compatibility with multiplication/Existence of multiplicative inverse/Associative property/Modulative property/Result. (Division property of inequality)

In consequence, the division property of inequality which states that:

`\forall\, a, b, c \in \mathbb{R}`. If
`c > 0`, then:

`a> b\,\longrightarrow a\cdot c > b\cdot c \,\lor\, a<b \longrightarrow a\cdot c < b\cdot c`

But if
`c < 0`, then:

`a> b\,\longrightarrow a\cdot c < b\cdot c \,\lor\, a<b \longrightarrow a\cdot c > b\cdot c`

Hence, correct answer is A.