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Solve the inequality and graph the solution.

4x + 2 < 3x - 4

(1 point)
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1 answer

To solve the inequality \(4x + 2 < 3x - 4\), follow these steps:

  1. Isolate the variable: Start by subtracting \(3x\) from both sides of the inequality.

    \[ 4x - 3x + 2 < -4 \]

    This simplifies to:

    \[ x + 2 < -4 \]

  2. Subtract 2 from both sides:

    \[ x < -4 - 2 \]

    Simplifying gives:

    \[ x < -6 \]

So the solution to the inequality is \(x < -6\).

Graphing the Solution

To graph this inequality on a number line:

  • Draw a number line.
  • Place an open circle at \(-6\) to denote that \(-6\) is not included in the solution.
  • Shade the line to the left of \(-6\) to indicate that all numbers less than \(-6\) are part of the solution.

Here's a representation of the graph:

<---|----|----|----|----|----|----|----|----|----|----|--->
   -8   -7   -6   -5   -4   -3   -2   -1    0    1    2
             (

Here, the parenthesis at \(-6\) indicates that \(-6\) itself is not included in the solution set.