Answered

Identify the property used in each step of solving the inequality [tex]7x + 4 \ \textless \ 46[/tex].

[tex]\[
\begin{array}{ll}
\text{Step} & \text{Inequality} \\
\text{1) } & 7x + 4 \ \textless \ 46 \\
\text{2) } & 7x \ \textless \ 42 \\
\text{3) } & x \ \textless \ 6 \\
\end{array}
\][/tex]

[tex]\[
\begin{array}{ll}
\text{Step} & \text{Property} \\
\text{1) } & \text{Given} \\
\text{2) } & \text{Subtraction Property of Inequality} \\
\text{3) } & \text{Division Property of Inequality} \\
\end{array}
\][/tex]



Answer :

GinnyAnswer
Let's solve the inequality [tex]\(7x + 4 < 46\)[/tex] and identify the properties used in each step.

Step 1) Given:
[tex]\[7x + 4 < 46\][/tex]

Step 2) Subtract 4 from both sides of the inequality. This uses the Subtraction Property of Inequality:
[tex]\[7x + 4 - 4 < 46 - 4\][/tex]
[tex]\[7x < 42\][/tex]

Step 3) Divide both sides of the inequality by 7. This uses the Division Property of Inequality:
[tex]\[\frac{7x}{7} < \frac{42}{7}\][/tex]
[tex]\[x < 6\][/tex]

So, the properties used in each step are:
Step 2) Subtraction Property of Inequality
Step 3) Division Property of Inequality

Now, let's fill out the table accordingly:

[tex]\[ \begin{array}{|c|c|} \hline \text{Step} & \text{Property}\\ \hline 1) & \text{Given} \\ \hline 7x + 4 < 46 & \\ 7x < 42 & \text{Subtraction Property of Inequality} \\ x < 6 & \text{Division Property of Inequality} \\ \hline \end{array} \][/tex]