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Michael solved this inequality as shown:

Step 1: [tex]\(-6(x+3)+10\ \textless \ -2\)[/tex]

Step 2: [tex]\(-6x-18+10\ \textless \ -2\)[/tex]

Step 3: [tex]\(-6x-8\ \textless \ -2\)[/tex]

Step 4: [tex]\(-6x\ \textless \ 6\)[/tex]

Step 5: [tex]\(x\ \textgreater \ -1\)[/tex]

Which property justifies the work shown between Step 3 and Step 4?

A. Transitive property
B. Division property of inequality
C. Distribution property
D. Addition property of inequality

Sagot :

GinnyAnswer
To determine which property justifies the work between step 3 and step 4, let's analyze the steps in detail:

1. Step 1: [tex]\(-6(x+3) + 10 < -2\)[/tex]
2. Step 2: Distribute [tex]\(-6\)[/tex] through the parenthesis: [tex]\(-6x - 18 + 10 < -2\)[/tex].
3. Step 3: Combine like terms: [tex]\(-6x - 8 < -2\)[/tex].
4. Step 4: To isolate [tex]\(x\)[/tex], we add [tex]\(8\)[/tex] to both sides of the inequality:
[tex]\[ -6x - 8 + 8 < -2 + 8 \implies -6x < 6 \][/tex]
5. Step 5: Divide both sides by [tex]\(-6\)[/tex] and reverse the inequality sign (as required when dividing by a negative number):
[tex]\[ x > -1 \][/tex]

The crucial question is about the justification of the step between Step 3 and Step 4. From Step 3 to Step 4, [tex]\(8\)[/tex] is added to both sides of the inequality. The property that allows for adding the same value to both sides of an inequality without changing the direction of the inequality is:

D. Addition Property of Inequality

Thus, the addition property of inequality justifies the work shown between step 3 and step 4.
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