Sam solved the following problem:
-4x + 5 > 29
-4x + 5 - 5 > 29 - 5
-4x > -24
-4x/-4 > -24/-4
x > 6
What were his two mistakes?
Sam forgot to reverse the inequality sign after dividing both
sides by -4
so ......
-4x/-4 < -24/-4
x < 6
Thank you!
@Reiny should there be a line under the "<" like this ≤?
Not unless it was there to start with.
mistake: -4x > -24 should be -4x > +24.
Answer: X < -6.
Sam made two mistakes in solving the problem.
Mistake 1: Sam incorrectly subtracted 5 from both sides of the inequality.
To solve inequalities, we need to perform the same operation on both sides to maintain the inequality. In this case, Sam tried to subtract 5 from both sides of the inequality:
-4x + 5 - 5 > 29 - 5
However, the correct operation should be to subtract 5 from only one side of the inequality:
-4x > 24
Mistake 2: Sam incorrectly divided both sides of the inequality by -4.
When dividing both sides of an inequality by a negative number, we need to flip the inequality sign. Sam divided both sides of the inequality by -4:
-4x/-4 > -24/-4
However, the correct operation should be to divide both sides of the inequality by a negative number and flip the inequality sign:
x < -6
So, the correct solution to the inequality -4x + 5 > 29 is x < -6.