These problems are pretty easy, but confusing (as stated in the subject line).
|2x+5|-x=10
|3x+4|-2x=11
I know there are supposed to be two answers for each problem, for the first problem I got 5 and for the second problem I got 7. I can't figure out the other answers for the problems. I would greatly appreciate any help I receive! Thanks!
Since it's absolute value,
2x+5=10+x OR
2x+5=-10-x
Just solve for x, and you get x=5, -5
Just do the same with the other!
I felt so stupid...I was solving the problems a completely different way! That's why I couldn't figure out the answers. Thanks for all your help, Mischa! :-)
I'm glad I could help! It's common to feel confused or struggle with math problems sometimes. Let me explain how to solve these absolute value equations step by step.
To solve the equation |2x+5|-x=10, we can start by isolating the absolute value term. Remember that the absolute value |2x+5| can be positive or negative, which is why we end up with two possible cases.
Case 1: |2x+5| = 2x+5
In this case, the absolute value is equal to the expression inside it. We can rewrite the equation as:
2x+5 - x = 10
Combine like terms:
x + 5 = 10
Subtract 5 from both sides:
x = 5
Case 2: |2x+5| = -(2x+5)
In this case, the absolute value is equal to the negation of the expression inside it. We can rewrite the equation as:
2x+5 + x = -10
Combine like terms:
3x + 5 = -10
Subtract 5 from both sides:
3x = -15
Divide both sides by 3:
x = -5
So for the first problem, the solutions are x = 5 and x = -5.
Now let's move on to the second problem, |3x+4|-2x=11.
Case 1: |3x+4| = 3x+4
Rewrite the equation as:
3x+4 - 2x = 11
Simplify the left side:
x + 4 = 11
Subtract 4 from both sides:
x = 7
Case 2: |3x+4| = -(3x+4)
Rewrite the equation as:
3x+4 + 2x = -11
Combine like terms:
5x + 4 = -11
Subtract 4 from both sides:
5x = -15
Divide both sides by 5:
x = -3
So for the second problem, the solutions are x = 7 and x = -3.
Remember, when solving absolute value equations, it's important to consider both cases (positive and negative) to find all possible solutions.