What's the solution to $-9 x+4<40$?
A) All real numbers
B) $x<-6$
C) $x>-4$
D) No solutions
Answer (1)
Subtract 4 from both sides: − 9 x < 36 .
Divide both sides by -9 and flip the inequality sign: -4"> x > − 4 .
The solution is all x greater than -4.
Therefore, the answer is -4}"> x > − 4 .
Explanation
Understanding the Inequality We are given the inequality − 9 x + 4 < 40 . Our goal is to isolate x and find the solution set.
Isolating the x term First, we subtract 4 from both sides of the inequality to get rid of the constant term on the left side: − 9 x + 4 − 4 < 40 − 4
− 9 x < 36
Solving for x Next, we divide both sides of the inequality by -9. Remember that when we divide or multiply an inequality by a negative number, we must flip the direction of the inequality sign: \frac{36}{-9}"> − 9 − 9 x > − 9 36
-4"> x > − 4
Interpreting the Solution The solution to the inequality is -4"> x > − 4 . This means that any value of x greater than -4 will satisfy the original inequality.
Examples
Imagine you're trying to figure out how many hours you can work this week. You need to earn more than $40, and after an initial $4 payment, you earn 9 p er h o u r . T h e in e q u a l i t y -9x + 4 < 40$ can be adapted to represent this situation. Solving it helps you determine the minimum number of hours you need to work to reach your goal. Understanding inequalities is crucial for budgeting, managing time, and making informed decisions in everyday financial planning.
