Question

solve and graph the following inequality: ( 1 geq 10 + x ) or ( -9x leq -7 )

Explanation:

Step1: Solve the first inequality

$$\begin{align*} 1&\geq10 + x\\ 1-10&\geq x\\ -9&\geq x\\ x&\leq - 9 \end{align*}$$

Step2: Solve the second inequality

$$\begin{align*} -9x&\leq - 7\\ x&\geq\frac{-7}{-9}\\ x&\geq\frac{7}{9} \end{align*}$$

Answer:

The solution of the inequality \(1\geq10 + x\) or \(-9x\leq - 7\) is \(x\leq - 9\) or \(x\geq\frac{7}{9}\).

To graph \(x\leq - 9\), we draw a closed circle at \(-9\) (because the inequality includes equality) and shade to the left. To graph \(x\geq\frac{7}{9}\), we draw a closed circle at \(\frac{7}{9}\) (because the inequality includes equality) and shade to the right.