To solve the inequality \( \frac{1}{3}x - 5 \geq -2 \), we will first isolate \( x \).
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Add \( 5 \) to both sides: \[ \frac{1}{3}x \geq 3 \]
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Multiply both sides by \( 3 \) (which is positive, so the inequality direction remains the same): \[ x \geq 9 \]
Now we know the solution to the inequality is \( x \geq 9 \).
To represent this on a number line, we need to show an open or closed circle at \( 9 \) and shade to the right since \( x \) includes \( 9 \) and all numbers greater than \( 9 \).
Now looking at your options (A, B, C, and D), it appears that the number lines cover different ranges of values.
Assuming Option C and D represent positive values, we would expect:
- The option that includes \( 9 \) and shades to the right from \( 9 \) is the correct representation of \( x \geq 9 \).
Please ensure to select the option that correctly highlights \( 9 \) and the shaded area to the right, indicating all values greater than or equal to \( 9 \).