Solve the given inequality and represent its solution on the number line. 18-6x>-12

Answer 1

To solve the inequality \( 18 - 6x > -12 \), follow these steps:

1. Isolate the term involving \( x \):

   Subtract \( 18 \) from both sides: \[ 18 - 6x - 18 > -12 - 18 \] This simplifies to: \[ -6x > -30 \]

2. Divide by -6:

   When dividing or multiplying both sides of an inequality by a negative number, the inequality sign must be flipped: \[ x < 5 \]

So the solution to the inequality \( 18 - 6x > -12 \) is: \[ x < 5 \]

Number Line Representation:

To represent this solution on a number line:

• Draw a number line.
• Mark the point \( 5 \) on the line.
• Since \( x \) is less than \( 5 \), use an open circle at \( 5 \) (indicating that \( 5 \) is not included in the solution) and shade the line to the left of \( 5 \).

Here's a visual representation:

<---|----|----|----|----|----|----|----|----|----|----|--->
    1    2    3    4    5    6    7    8    9   10
         (open circle at 5)

The shaded portion to the left of \( 5 \) indicates all values of \( x \) that are less than \( 5 \).