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

Answer:

A. Division property of inequality.

Step-by-step 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:

$a> b\,\longrightarrow a\cdot c > b\cdot c \,\lor\, a$

But if $c < 0$, then:

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

Hence, correct answer is A.