Question

solve the inequality. express your answer using interval notation. graph the solution set.$(x + 5)(x - 6) > (x - 2)(x + 2)$the solution to the inequality is $square$.(type your answer in interval notation. use integers or fractions for any numbers in the expression)

Explanation:

Step1: Expand both sides

Left: $(x+5)(x-6) = x^2 -6x +5x -30 = x^2 -x -30$
Right: $(x-2)(x+2) = x^2 -4$

Step2: Rearrange inequality

Subtract $x^2 -4$ from both sides:
$x^2 -x -30 - (x^2 -4) > 0$
Simplify: $-x -26 > 0$

Step3: Isolate the variable

Add 26 to both sides: $-x > 26$
Multiply by -1 (reverse inequality): $x < -26$

Step4: Write in interval notation

All real numbers less than -26: $(-\infty, -26)$

Answer:

$(-\infty, -26)$

For the graph: Draw a number line, place an open circle at -26, and shade all regions to the left of -26.