Answer:
A. Division property of inequality.
Step-by-step explanation:
Let be [tex]2\cdot x > 10[/tex], we proceed to show the appropriate procedure to step 4:
1) [tex]2\cdot x >10[/tex] Given
2) [tex]x > 5[/tex] 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:
[tex]\forall\, a, b, c \in \mathbb{R}[/tex]. If [tex]c > 0[/tex], then:
[tex]a> b\,\longrightarrow a\cdot c > b\cdot c \,\lor\, a<b \longrightarrow a\cdot c < b\cdot c[/tex]
But if [tex]c < 0[/tex], then:
[tex]a> b\,\longrightarrow a\cdot c < b\cdot c \,\lor\, a<b \longrightarrow a\cdot c > b\cdot c[/tex]
Hence, correct answer is A.
