Question

select the values that are solutions to the inequality $x^2 + 3x - 4 > 0$.-6-205done

Explanation:

Step1: Factor the quadratic

$x^2 + 3x - 4 = (x+4)(x-1)$

Step2: Find critical points

Set $(x+4)(x-1)=0$, so $x=-4$ or $x=1$

Step3: Test intervals

• For $x < -4$: $(-6+4)(-6-1)=(-2)(-7)=14>0$, satisfies inequality
• For $-4 < x < 1$: $(-2+4)(-2-1)=(2)(-3)=-6<0$; $(0+4)(0-1)=(4)(-1)=-4<0$, does not satisfy
• For $x > 1$: $(5+4)(5-1)=(9)(4)=36>0$, satisfies inequality

Answer:

-6, 5