Solve and graph this inequality: 5x -10 < 2x - 4

Answer 1

To solve the inequality \( 5x - 10 < 2x - 4 \), we can follow these steps:

1. Isolate the variable term on one side: Start by getting all the \( x \) terms on one side and the constant terms on the other.

   \[ 5x - 2x < -4 + 10 \]

   This simplifies to:

   \[ 3x < 6 \]

2. Divide by 3: Divide both sides of the inequality by 3 to solve for \( x \).

   \[ x < 2 \]

Now we have the solution: \( x < 2 \).

Graphing the Inequality

To graph the inequality \( x < 2 \):

1. Draw a number line.
2. Plot the point at 2 and use an open circle to indicate that 2 is not included in the solution (because it's a strict inequality).
3. Shade the region to the left of 2 to indicate all the values of \( x \) that are less than 2.

Here's an illustration of that:

<---(----|----|----|----|----|----|----|----|----|----|----|---->
      -3   -2   -1    0    1    2    3    4    5

The shaded area extends to the left of 2, reflecting all values of \( x \) that are less than 2.