Find answers to your questions faster and easier with IDNLearn.com. Join our Q&A platform to receive prompt and accurate responses from knowledgeable professionals in various fields.
Sagot :
To solve the given equation step-by-step and provide the correct justifications, let's break down the process:
1. Start with the given equation:
[tex]\[ 4(x + 5) = 2x + 2 \][/tex]
Justification: Given
2. Apply the Distributive Property to the left-hand side of the equation to expand it:
[tex]\[ 4x + 20 = 2x + 2 \][/tex]
Justification: Distributive Property
3. Subtract [tex]\(2x\)[/tex] from both sides of the equation to move the variable terms to one side:
[tex]\[ 2x + 20 = 2 \][/tex]
Justification: Subtraction Property of Equality
4. Subtract 20 from both sides of the equation to isolate the variable term:
[tex]\[ 2x = -18 \][/tex]
Justification: Subtraction Property of Equality
5. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = -9 \][/tex]
Justification: Division Property of Equality
Given these steps, let's fill in the missing justifications in the provided table:
[tex]\[ \begin{tabular}{|l|l|} \hline Mathematical Statement & Justification \\ \hline $4(x+5)=2 x+2$ & Given \\ \hline $4x+20=2x+2$ & Distributive Property \\ \hline $2x+20=2$ & Subtraction Property of Equality \\ \hline $2x=-18$ & Subtraction Property of Equality \\ \hline $x=-9$ & Division Property of Equality \\ \hline \end{tabular} \][/tex]
So, the correct order of justifications is:
Distributive Property, Subtraction Property of Equality, Subtraction Property of Equality, Division Property of Equality
1. Start with the given equation:
[tex]\[ 4(x + 5) = 2x + 2 \][/tex]
Justification: Given
2. Apply the Distributive Property to the left-hand side of the equation to expand it:
[tex]\[ 4x + 20 = 2x + 2 \][/tex]
Justification: Distributive Property
3. Subtract [tex]\(2x\)[/tex] from both sides of the equation to move the variable terms to one side:
[tex]\[ 2x + 20 = 2 \][/tex]
Justification: Subtraction Property of Equality
4. Subtract 20 from both sides of the equation to isolate the variable term:
[tex]\[ 2x = -18 \][/tex]
Justification: Subtraction Property of Equality
5. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = -9 \][/tex]
Justification: Division Property of Equality
Given these steps, let's fill in the missing justifications in the provided table:
[tex]\[ \begin{tabular}{|l|l|} \hline Mathematical Statement & Justification \\ \hline $4(x+5)=2 x+2$ & Given \\ \hline $4x+20=2x+2$ & Distributive Property \\ \hline $2x+20=2$ & Subtraction Property of Equality \\ \hline $2x=-18$ & Subtraction Property of Equality \\ \hline $x=-9$ & Division Property of Equality \\ \hline \end{tabular} \][/tex]
So, the correct order of justifications is:
Distributive Property, Subtraction Property of Equality, Subtraction Property of Equality, Division Property of Equality
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.