Questions: Solve the inequality. Graph the solution set, and write the solution set in set-builder notation and interval notation. Write numbers as simplified fractions or integers. [ -6<5(c-9)+9 ] The solution set in set-builder notation is . - - - - - - < - > - - <= - - >= - - - x 0 - - -

Solve the inequality. Graph the solution set, and write the solution set in set-builder notation and interval notation. Write numbers as simplified fractions or integers.
[
-6<5(c-9)+9
]

The solution set in set-builder notation is .

-  -  - 
-    -   - <
-  > -   -  <= -   -  >= - 
-      
-  x   0 
-  -  -
Transcript text: Solve the inequality. Graph the solution set, and write the solution set in set-builder notation and interval notation. Write numbers as simplified fractions or integers. \[ -6<5(c-9)+9 \] The solution set in set-builder notation is $\square$ . \begin{tabular}{|ccc|} \hline$\frac{\square}{\square}$ & {$[\square \mid \square]$} & $\square<\square$ \\ $\square>\square$ & $\square \leq \square$ & $\square \geq \square$ \\ $\}$ & $\mathbb{R}$ & \\ \hline$\times$ & 0 \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Simplify the Inequality

Start by simplifying the inequality: \[ -6 < 5(c-9) + 9 \]

Distribute the 5: \[ -6 < 5c - 45 + 9 \]

Combine like terms: \[ -6 < 5c - 36 \]

Step 2: Solve for \( c \)

Add 36 to both sides: \[ 30 < 5c \]

Divide both sides by 5: \[ 6 < c \]

Final Answer

The solution set in set-builder notation is \(\{ c \mid c > 6 \}\).

Step 3: Interval Notation

The solution set in interval notation is \((6, \infty)\).

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