Question

1. solve and graph ( x - 6 leq 15 + 8x )

Explanation:

Step1: Move variables to one side

Subtract \(x\) from both sides:
\(x - 6-x\leq15 + 8x-x\)
\(-6\leq15 + 7x\)

Step2: Isolate the term with \(x\)

Subtract \(15\) from both sides:
\(-6-15\leq15 + 7x-15\)
\(-21\leq7x\)

Step3: Solve for \(x\)

Divide both sides by \(7\):
\(\frac{-21}{7}\leq\frac{7x}{7}\)
\(-3\leq x\) or \(x\geq - 3\)

Step4: Graph the solution

On the number - line, put a closed circle at \(x = - 3\) (because the inequality is \(\leq\) which includes equality) and shade to the right (since \(x\) is greater than or equal to \(-3\)).

Answer:

The solution of the inequality \(x - 6\leq15 + 8x\) is \(x\geq - 3\). On the number - line, there is a closed circle at \(-3\) and the line is shaded to the right of \(-3\).