Answered

Join the growing community of curious minds on IDNLearn.com and get the answers you need. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.

Select the correct answer.

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 :

GinnyAnsweridn
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.
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.