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Emilia solved this inequality as shown:
[tex]\[
\begin{array}{rrl}
\text{Step 1:} & 2(x-3) & \ \textgreater \ x + 9 \\
\text{Step 2:} & 2x - 6 & \ \textgreater \ x + 9 \\
\text{Step 3:} & x - 6 & \ \textgreater \ 9 \\
\text{Step 4:} & x & \ \textgreater \ 15
\end{array}
\][/tex]

What property justifies the work between step 2 and step 3?

A. Transitive property of inequality

B. Distributive property of inequality

C. Subtraction property of inequality

D. Division property of inequality

Sagot :

GinnyAnswer
Let's analyze what Emilia did between Step 2 and Step 3.

Given:
[tex]\[ \begin{array}{rrl} \text{Step 2:} & 2x - 6 &> x + 9 \end{array} \][/tex]

To go from Step 2 to Step 3, Emilia transformed the expression [tex]\(2x - 6 > x + 9\)[/tex] to [tex]\(x - 6 > 9\)[/tex]. Here, you can see that she needed to eliminate the [tex]\(x\)[/tex] term from the right side of the inequality and simplify it further.

In order to perform this transformation, she subtracted [tex]\(x\)[/tex] from both sides of the inequality. This is an example of the subtraction property of inequality, which states that if you subtract the same value from both sides of an inequality, the inequality remains valid.

Thus, the property that justifies the work between Step 2 and Step 3 is the:

Subtraction property of inequality.
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