Instead of multiplying first, add 5 to all three members. That will give you 3/(x - 1) in the middle of the inequality. Remember, you can always add any amount to both (or all) sides of an inequality.lovemake1 said:Homework Statement
l [3/(x-1)] - 5l < 4
Homework Equations
The Attempt at a Solution
My 1st step was to make the inequality like this. -4 < 3/(x-1) - 5 < 4
and then i multiplied (x-1) to both left and right side and as well as to the 5.
lovemake1 said:but in the end, my result turns out to be really wrong.
I got 9/5 < x < 4/5
which is not possible.
please help.
Here (above). -4 + 5 isn't -1.lovemake1 said:even if i add 5 to both side, i still get a very weird inequality.
i'll show my steps so you can see where i went wrong
-1 < 3(x-1) < 9
When you multiply by x - 1 you need to have two separate inequalities, as I explained earlier.lovemake1 said:-1(x-1) < 3 < 9(x-1)
lovemake1 said:-x + 1 < 3 < 9x -9
-2 < -8x < -12
2/8 > x > 12/8
12/8 < x < 2/8
where did i possibly go wrong? please help.
Absolute value inequality is a type of mathematical inequality that involves the absolute value of a variable. It is used to express relationships between quantities that have both positive and negative values.
To solve an absolute value inequality, you first isolate the absolute value expression on one side of the inequality sign. Then, you split the inequality into two cases, one for when the expression inside the absolute value is positive, and one for when it is negative. Finally, you solve each case separately and combine the solutions to get the final solution.
The main difference between absolute value equations and inequalities is that equations have an equal sign (=) while inequalities have an inequality sign (≤ or ≥). In other words, equations express that two quantities are equal, while inequalities express that one quantity is less than or greater than another.
Absolute value is important in real-world applications because it allows us to represent and analyze quantities that can have both positive and negative values. This is particularly useful in situations where we need to measure distance, such as in physics or engineering problems.
Yes, absolute value inequalities can have more than one solution. In fact, there can be infinitely many solutions, depending on the complexity of the inequality. It is important to carefully check the solutions obtained and make sure they satisfy the original inequality.