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Express in interval notation $-6a+30 \leq 6(a-5)$

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Write an equation from words

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Q. Express in interval notation

-6a+30 \leq 6(a-5)

Write Inequality with Distributed Term: Now, let's write the inequality with the distributed term. $\newline$ $-6a + 30 \leq 6a - 30$
Addition to Get 'a' Terms Together: Next, we add $6a$ to both sides to get the 'a' terms on one side. $\newline$ $-6a + 6a + 30 \leq 6a + 6a - 30$ $\newline$ This simplifies to: $\newline$ $30 \leq 12a - 30$
Addition to Isolate 'a' Term: Then, we add $30$ to both sides to isolate the 'a' term. $\newline$ $30 + 30 \leq 12a - 30 + 30$ $\newline$ This gives us: $\newline$ $60 \leq 12a$
Division to Solve for 'a': Now, we divide both sides by $12$ to solve for 'a'. $\newline$ $\frac{60}{12} \leq \frac{12a}{12}$ $\newline$ This simplifies to: $\newline$ $5 \leq a$
Express in Interval Notation: Finally, we express this inequality in interval notation. $\newline$ The inequality $5 \leq a$ means that ' $a$ ' is greater than or equal to $5$ . $\newline$ So, in interval notation, this is written as: $\newline$ $[5, \infty)$

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