Question

solve the linear inequality for ( x ) and graph the answer in the number line. then write the solution in inequality notation.

( 3 < x - 3 )

show your work here

hint: to add inequalities ( (<,>, leq, geq) ), type \less\ or \greater\

Explanation:

Step1: Isolate the variable \(x\)

Add \(3\) to both sides of the inequality \(3\lt x - 3\).
Using the addition property of inequalities (\(a\lt b\) implies \(a + c\lt b + c\)), we have \(3+3\lt x-3 + 3\).

Step2: Simplify the inequality

Simplify \(3 + 3\) and \(x-3 + 3\).
\(6\lt x\) (which is equivalent to \(x>6\))

Answer:

The solution in inequality notation is \(x > 6\). On the number - line, we have an open circle at \(x = 6\) (because \(6\) is not included in the solution set, since the inequality is \(>\)) and an arrow pointing to the right (towards larger values of \(x\)).