To solve the inequality \( 1 \geq \frac{x}{3} \), we can follow these steps:
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Multiply both sides by 3: Since we are multiplying by a positive number, the direction of the inequality remains the same. \[ 3 \cdot 1 \geq 3 \cdot \frac{x}{3} \] \[ 3 \geq x \] This can also be written as: \[ x \leq 3 \]
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Determine the solution set: The solution to the inequality \( x \leq 3 \) means that \( x \) can take any value less than or equal to 3.
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Graph the solution on the number line:
- Mark the number 3 on the number line.
- Since \( x \) is less than or equal to 3, you will shade all the numbers to the left of 3, including 3 itself (usually denoted with a closed dot at 3 to show that it is included).
Here’s how you would visualize it on the number line from -12 to 12:
-12 -10 -8 -6 -4 -2 0 2 3 4 6 8 10 12
|---------|--------|--------|--------|--------|-------|-------|-------|-------|-------|-------|-------|
<--------- (closed dot at 3)=========================>
The arrow on the left signifies that the shading goes indefinitely in the negative direction (to the left of 3). The closed dot at 3 indicates that 3 is part of the solution set.
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