To solve the inequality \(-3x + 1 \leq -47\), we can follow these steps:
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Isolate the term with \(x\): Start by subtracting 1 from both sides of the inequality: \[ -3x + 1 - 1 \leq -47 - 1 \] This simplifies to: \[ -3x \leq -48 \]
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Divide by -3: When you divide or multiply an inequality by a negative number, you must reverse the inequality sign: \[ x \geq \frac{-48}{-3} \] This simplifies to: \[ x \geq 16 \]
Now that we have the solution \(x \geq 16\), we can graph it on a number line.
Graphing the solution:
- Draw a number line.
- Place an open circle (or dot) at the point 16 to represent that the solution includes 16 and all numbers greater than 16.
- Shade the region to the right of 16 to indicate all numbers greater than or equal to 16 are part of the solution.
Here is how it would look visually:
<---|----|----|----|----|----|----|----|----|----|----|----|----|--->
0 1 2 3 4 5 6 7 8 9 10 11 12 ... 16
●================>
(Shade to the right)
In this representation, the point 16 is marked with a solid circle (if closed) to show that 16 is included in the solution. If using a closed dot, the inequality would reflect that \(x\) can equal 16.
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