Question

solve the inequality below and choose the correct graph that represents the answer.
$$ - 1 - 9 x - 6 > - 11 - 8 x $$

Explanation:

Step1: Simplify the left - hand side

Combine like terms: \(-1-6-9x=-7 - 9x\). So the inequality becomes \(-7-9x>-11 - 8x\).

Step2: Add \(9x\) to both sides

Using the addition property of inequalities: \(-7-9x + 9x>-11-8x + 9x\), which simplifies to \(-7>x - 11\).

Step3: Add \(11\) to both sides

Using the addition property of inequalities: \(-7+11>x-11 + 11\). So \(4>x\) or \(x < 4\).

When graphing \(x < 4\) on a number line, we use an open circle at \(x = 4\) (because \(x\) is not equal to \(4\)) and the arrow points to the left.

Answer:

The second option (the one with an open circle at \(4\) and the arrow pointing to the left) is the correct graph.