Questions: Solve the following inequality and graph the solution set. -4x + 10 <= 9

Solve the following inequality and graph the solution set.
 -4x + 10  <= 9
Transcript text: Quiz Solve the following inequality and graph the solution set. \[ |-4 x+10| \leq 9 \]
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Solution

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Solution Steps

Step 1: Solve the absolute value inequality

To solve the inequality 4x+109|-4x + 10| \leq 9, we need to consider two cases:

  1. 4x+109-4x + 10 \leq 9
  2. (4x+10)9-(-4x + 10) \leq 9 which simplifies to 4x1094x - 10 \leq 9
Step 2: Solve the first case

4x+109 -4x + 10 \leq 9 Subtract 10 from both sides: 4x1 -4x \leq -1 Divide by -4 (and reverse the inequality sign): x14 x \geq \frac{1}{4}

Step 3: Solve the second case

4x109 4x - 10 \leq 9 Add 10 to both sides: 4x19 4x \leq 19 Divide by 4: x194 x \leq \frac{19}{4}

Final Answer

Combining both cases, the solution set is: 14x194 \frac{1}{4} \leq x \leq \frac{19}{4}

{"axisType": 3, "coordSystem": {"xmin": -1, "xmax": 6, "ymin": -1, "ymax": 2}, "commands": ["y = 0", "y = 1"], "latex_expressions": ["frac14leqxleqfrac194\\frac{1}{4} \\leq x \\leq \\frac{19}{4}"]}

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