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What is the solution to the inequality below?
[tex]\[
\frac{x}{9} + 3 \ \textless \ 4
\][/tex]
A. [tex]\( x \ \textless \ 9 \)[/tex] B. [tex]\( x \ \textless \ 1 \)[/tex] C. [tex]\( x \ \textless \ 7 \)[/tex] D. [tex]\( x \ \textless \ 10 \)[/tex]
To solve the inequality [tex]\( \frac{x}{9} + 3 < 4 \)[/tex], let's go through the steps methodically:
1. Start with the given inequality: [tex]\[
\frac{x}{9} + 3 < 4
\][/tex]
2. Isolate the term involving [tex]\(x\)[/tex]: - Subtract 3 from both sides of the inequality to get rid of the constant term on the left side. [tex]\[
\frac{x}{9} + 3 - 3 < 4 - 3
\][/tex] Simplifying this, we get: [tex]\[
\frac{x}{9} < 1
\][/tex]
3. Solve for [tex]\(x\)[/tex]: - To isolate [tex]\(x\)[/tex], multiply both sides of the inequality by 9. [tex]\[
\left(\frac{x}{9}\right) \cdot 9 < 1 \cdot 9
\][/tex] Simplifying this, we get: [tex]\[
x < 9
\][/tex]
Therefore, the solution to the inequality [tex]\( \frac{x}{9} + 3 < 4 \)[/tex] is [tex]\( x < 9 \)[/tex]. Thus, the correct answer is:
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