Question

solve the compound inequality and choose the correct graph below.

(-x + 5geq9x - 15) and (3x - 9lt5x + 3)

Explanation:

Step1: Solve the first inequality \(-x + 5\geq9x-15\)

Add \(x\) to both sides: \(5\geq10x - 15\).
Add \(15\) to both sides: \(20\geq10x\).
Divide both sides by \(10\): \(x\leq2\).

Step2: Solve the second inequality \(3x - 9\lt5x+3\)

Subtract \(3x\) from both sides: \(-9\lt2x + 3\).
Subtract \(3\) from both sides: \(-12\lt2x\).
Divide both sides by \(2\): \(-6\lt x\).

Answer:

The solution of the compound inequality is \(-6\lt x\leq2\). So the correct graph is the one where there is an open - circle at \(-6\) (because \(x\gt - 6\)) and a closed - circle at \(2\) (because \(x\leq2\)) with a line segment connecting them.