do not break it up when solving -51 is less than or equal to 5x-1 is less than 4 solve give solution and graph

Answer 1

To solve the compound inequality \(-51 \leq 5x - 1 < 4\) without breaking it up, you can treat it as one entire inequality. We will solve it step by step.

1. Solve the left side of the inequality: \[ -51 \leq 5x - 1 \] Add 1 to both sides: \[ -51 + 1 \leq 5x \] \[ -50 \leq 5x \] Divide by 5: \[ -10 \leq x \quad \text{or} \quad x \geq -10 \]

2. Solve the right side of the inequality: \[ 5x - 1 < 4 \] Add 1 to both sides: \[ 5x < 4 + 1 \] \[ 5x < 5 \] Divide by 5: \[ x < 1 \]

3. Combine the results: From the two parts, we have: \[ -10 \leq x < 1 \] Therefore, the solution to the compound inequality is: \[ -10 \leq x < 1 \]

4. Graph the solution: To graph the solution on the number line:

   • Draw a line with numbers from -10 to 1.
   • Place a closed dot at -10 (indicating -10 is included).
   • Place an open dot at 1 (indicating 1 is not included).
   • Shade the region between -10 and 1.

Here's a representation of the graph:

<-----●==================○----->
      -10                  1

Final Result:

The solution to the inequality \(-51 \leq 5x - 1 < 4\) is: \[ x \in [-10, 1) \]