Question

solve the inequality. express your answer using interval notation. graph the solution set. (x + 6)(x - 7)>(x - 3)(x + 3). the solution to the inequality is . (type your answer in interval notation. use integers or fractions for any numbers in the expression. simplify your answer.) graph the inequality. choose the correct graph below.

Explanation:

Step1: Expand both sides

Expand \((x + 6)(x - 7)\) and \((x - 3)(x+3)\) using FOIL method.
\((x + 6)(x - 7)=x^{2}-7x+6x - 42=x^{2}-x - 42\)
\((x - 3)(x + 3)=x^{2}-9\)
The inequality becomes \(x^{2}-x - 42>x^{2}-9\).

Step2: Simplify the inequality

Subtract \(x^{2}\) from both sides of the inequality:
\(x^{2}-x - 42-x^{2}>x^{2}-9 - x^{2}\)
\(-x-42>-9\)

Step3: Isolate the variable

Add 42 to both sides: \(-x-42 + 42>-9 + 42\), so \(-x>33\).
Multiply both sides by - 1 and reverse the inequality sign: \(x<-33\).

Answer:

The solution in interval - notation is \((-\infty,-33)\). The correct graph is the one with an open - circle at \(-33\) and an arrow pointing to the left. Among the given graphs, if there is a graph with an open - circle at \(-33\) and an arrow pointing left, that is the correct graph.