-4/10x -9 < 9/10 = x < 24 3/4
Did I do this right? was solving for the inequality and the -4/10x is together.
-4/10x - 9 < 9/10
multiply by 10
-4x - 90 < 9
-4x < 99
x > -99/4
or
x > -24 3/4
Looks like you dropped the minus sign somewhere
Too bad you couldn't be bothered to show your work...
I hope your text did not print it this way. The "= x < 24 3/4" is quite confusing.
I will read it as:
(-4/10)x -9 < 9/10 AND x < 24 3/4
first part times 10
-4x - 90 < 9 and x < 99/4
-4x < 99 and x < 99/4
x > -99/4 and x < 99/4
or
-99/4 < x < 99/4
To determine if you solved the inequality correctly, let's break it down step by step.
Given inequality: -4/10x - 9 < 9/10 < x < 24 3/4
First, let's simplify the expression -4/10x - 9 < 9/10.
Step 1: Distribute the negative sign to the fraction -4/10x.
-4/10x - 9 < 9/10
Step 2: Simplify the expression by multiplying both sides by 10 to eliminate the fractions.
-4x - 90 < 9
Step 3: Add 90 to both sides to isolate the variable.
-4x < 99
Step 4: Divide both sides by -4. Since we are dividing by a negative number, we must reverse the inequality sign.
x > -99/4 (or x > -24.75)
Now, let's verify if your solution matches the correct solution.
The correct solution is x > -24.75.
Given range: -24.75 < x < 24 3/4
Comparing the given range to your solution, we can see that you correctly obtained the lower limit by simplifying the inequality. However, your upper limit is not written in the correct format. The mixed number 24 3/4 can be simplified to 99/4. So, the correct range is -24.75 < x < 99/4.
In summary, you correctly simplified the inequality but didn't express the upper limit properly. The correct solution is -24.75 < x < 99/4.