Question

quiz: algebra 2 m01t03 quiz
solve for x and graph the solution.
-2x² + 14x - 24 < 0
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Make the inequality an equation.

$-2x^{2}+14x - 24=0$

Step2: Divide by - 2.

$x^{2}-7x + 12 = 0$

Step3: Factor the quadratic equation.

$(x - 3)(x - 4)=0$

Step4: Solve for x.

$x=3$ or $x = 4$

Step5: Test intervals.

Test $x=2$: $-2(2)^{2}+14(2)-24=-8 + 28-24=-4<0$, so $x<3$ is part of the solution.
Test $x = 3.5$: $-2(3.5)^{2}+14(3.5)-24=-24.5+49 - 24=0.5>0$, so $3Test $x=5$: $-2(5)^{2}+14(5)-24=-50 + 70-24=-4<0$, so $x>4$ is part of the solution.

Answer:

The solution of the inequality $-2x^{2}+14x - 24<0$ is $x<3$ or $x>4$. On the number - line, we have open circles at $x = 3$ and $x = 4$, and the shaded regions are to the left of $x = 3$ and to the right of $x = 4$.