Question

solve for ( x ) and graph the solution on the number line below.

( 2 x - 6 geq 4 ) and ( 18 geq 2 x - 6 )

answer attempt 1 out of 3

inequality notation:

number line:

Explanation:

Step1: Solve \(2x - 6\geq4\)

Add \(6\) to both sides: \(2x-6 + 6\geq4 + 6\), so \(2x\geq10\).
Divide both sides by \(2\): \(x\geq5\).

Step2: Solve \(18\geq2x - 6\)

Add \(6\) to both sides: \(18+6\geq2x-6 + 6\), so \(24\geq2x\).
Divide both sides by \(2\): \(12\geq x\) or \(x\leq12\).

Answer:

Inequality Notation: \(5\leq x\leq12\)

To graph on the number - line:

• Plot a closed circle at \(x = 5\) (because \(x\) can be equal to \(5\) as per \(x\geq5\)) and draw a line to the right.
• Plot a closed circle at \(x = 12\) (because \(x\) can be equal to \(12\) as per \(x\leq12\)) and draw a line to the left. The overlapping region (from \(x = 5\) to \(x = 12\)) is the solution set.