20 - 4/5x greater than or equal to 16. I did this and got the answer x greater than or equal to -5 but the correct answer is said to be x is less than or equal to 5. i am not sure what i did wrong. thanks
I will first assume the second term is 4x/5 and not 4/(5x)
If 20 - 4x/5 >or= 16
-4x/5 >or= -4
-4x >or= 20
Now here is where you probably went wrong: When you multiply or divide both sides of an inequality by a negative number, you must change the direction of the > or < sign.
Divide by -4 and you get
x <or= 5
To solve the inequality, let's follow these steps:
1. Start by subtracting 16 from both sides of the inequality: 20 - 4/5x - 16 ≥ 0. Simplifying gives us 4 - 4/5x ≥ 0.
2. Next, let's simplify the expression by multiplying both sides by 5 to get rid of the fraction: 5(4 - 4/5x) ≥ 0 * 5. Simplifying further, we have 20 - 4x ≥ 0.
3. Now, let's subtract 20 from both sides: 20 - 20 - 4x ≥ 0 - 20. Simplifying gives us -4x ≥ -20.
4. To isolate x, we need to divide both sides by -4. However, since we are dividing by a negative number, the inequality symbol will flip: -4x/-4 ≤ -20/-4. Simplifying further, we have x ≤ 5.
Therefore, the correct solution is x ≤ 5, not x ≥ -5. Double-check your calculations, and make sure you correctly applied the steps outlined above.
To solve inequalities like the one you provided, we need to follow a specific order of operations, just like with equations. Let's break down the steps to correctly solve this inequality.
Given: 20 - (4/5)x ≥ 16.
Step 1: Start by subtracting 20 from both sides of the inequality to isolate the term with the variable:
20 - (4/5)x - 20 ≥ 16 - 20.
This simplifies to:
-(4/5)x ≥ -4.
Step 2: To get rid of the negative sign in front of the term, we need to multiply both sides of the inequality by -1. Since we are multiplying by a negative number, the inequality sign must also be flipped:
(-(4/5)x) * (-1) ≤ (-4) * (-1).
This simplifies to:
(4/5)x ≤ 4.
Step 3: Now, we need to isolate the variable x. Since x is being divided by (4/5), we can multiply both sides by its reciprocal, which is (5/4):
(4/5)x * (5/4) ≤ 4 * (5/4).
This simplifies to:
x ≤ 5.
So, the correct solution is x ≤ 5, not x ≥ -5, as you initially calculated.
Inequalities differ from equations because multiplying (or dividing) both sides by a negative number flips the inequality sign. Make sure to double-check your steps while solving inequalities, paying close attention to the signs and operations used.
20 - (4/5)x ≥ 16 ??
-(4/5)x ≥ -4 now multiply both sides by -1 and change direction of arrow
(4/5) x ≤ 4
x ≤ 5