Question

question 7 (1 point) which shows the solution to -9x + 11 > -25?
a x > 4
b x = 4
c x > -4
d x = -4

Explanation:

Step1: Solve the inequality \(-9x + 11 > -25\)

Subtract 11 from both sides: \(-9x + 11 - 11 > -25 - 11\)
Simplify: \(-9x > -36\)

Step2: Divide both sides by -9 (remember to reverse the inequality sign)

\(\frac{-9x}{-9} < \frac{-36}{-9}\)
Simplify: \(x < 4\) Wait, no, wait. Wait, let's check again. Wait, original inequality: \(-9x + 11 > -25\)
Subtract 11: \(-9x > -25 - 11 = -36\)
Divide by -9: when dividing by a negative number, inequality sign flips. So \(x < \frac{-36}{-9} = 4\). Wait, but the options are a: \(x>4\), b: \(x<4\), c: \(x>-4\), d: \(x<-4\). Wait, maybe I made a mistake. Wait, let's re-express the inequality. Wait, maybe the original inequality is \(-9x + 11 > -25\)? Wait, no, maybe it's a typo, but let's solve again. Wait, \(-9x + 11 > -25\)
Subtract 11: \(-9x > -36\)
Divide by -9: \(x < 4\) (since dividing by negative reverses the inequality). So the solution is \(x < 4\), which is option b? Wait, but let's check the options again. The options are:
a: \(x > 4\)
b: \(x < 4\)
c: \(x > -4\)
d: \(x < -4\)
Wait, maybe I misread the inequality. Wait, maybe the inequality is \(-9x + 11 > 25\)? No, the user wrote "-9x + 11 > -25". Wait, let's check the arithmetic again. \(-9x + 11 > -25\)
Subtract 11: \(-9x > -36\)
Divide by -9: \(x < 4\) (because -36 divided by -9 is 4, and dividing by negative flips the inequality). So the solution is \(x < 4\), which is option b. Wait, but let's confirm. Let's plug x=0 into the original inequality: \(-9(0) + 11 = 11 > -25\), which is true. x=0 is less than 4, so that works. x=5: \(-9(5) + 11 = -45 + 11 = -34 > -25\)? No, -34 is not greater than -25. So x=5 (which is greater than 4) does not work. x=3 (less than 4): \(-27 + 11 = -16 > -25\), which is true. So yes, x < 4 is the solution, which is option b.

Answer:

b. \(x < 4\)