Question

solve for ( x ) and graph the solution on the number line below.
( 20 geq 5x + 10 ) or ( 65 leq 5x + 10 )
answer attempt 1 out of 2

inequality notation: ( x leq 2 ) or ( x geq 11 )
number line:

Explanation:

Step1: Solve the first inequality \(20\geq5x + 10\)

Subtract \(10\) from both sides:
\(20-10\geq5x+10 - 10\)
\(10\geq5x\)
Divide both sides by \(5\):
\(\frac{10}{5}\geq\frac{5x}{5}\)
\(2\geq x\) or \(x\leq2\)

Step2: Solve the second inequality \(65\leq5x + 10\)

Subtract \(10\) from both sides:
\(65 - 10\leq5x+10-10\)
\(55\leq5x\)
Divide both sides by \(5\):
\(\frac{55}{5}\leq\frac{5x}{5}\)
\(11\leq x\) or \(x\geq11\)

Answer:

The solution in inequality notation is \(x\leq2\) or \(x\geq11\). On the number - line, for \(x\leq2\), we have a closed circle at \(x = 2\) and an arrow pointing to the left. For \(x\geq11\), we have a closed circle at \(x = 11\) and an arrow pointing to the right.