I need to know if I did this problem correctly:
5. Solve for x in |x - 3| >8
Work: |x - 3| >8
|x| > 8 +3
Anwer= x > 11
I also need help with these 2:
15. Comepare the quantity in Column A with the quantity in Column B.
Column A- slope of y = 2x +2
Column B- slope of 2y = 3x + 9
a. The quantity in Column A is greater.
b. The quantity in Column B is greater.
c. the two quantities are equal
d. the relationship cannot be determined on the basis of the information supplied.
22. Simplify .5(2.3 + 25)/ 1.5 to the nearest tenth.
Thanks
-MC
I don't know about 15.
5 looks right.
22. .5(27.3)/1.5
Divide both numerator and denominator by .5
25.3/3 = ?
Let's go through each of your questions step by step:
1. Solving |x - 3| > 8:
To solve this inequality, you need to consider two cases: x - 3 > 8 and x - 3 < -8.
Case 1: x - 3 > 8
Adding 3 to both sides of the inequality, we get:
x > 11
Case 2: x - 3 < -8
Adding 3 to both sides of the inequality, we get:
x < -5
Therefore, the solution to the inequality |x - 3| > 8 is x > 11 or x < -5. So, your initial work is incorrect. The correct answer is not just x > 11, but rather x > 11 or x < -5.
2. Comparing the slopes in Column A and Column B:
To determine which quantity is greater, you need to compare the slopes of the given equations.
For Column A, the slope of y = 2x + 2 is 2.
For Column B, you need to rearrange the equation 2y = 3x + 9 to get it in the form y = mx + b, where m represents the slope:
Divide both sides of the equation by 2:
y = (3x + 9)/2
Comparing the coefficients of x in both equations, you can see that the slope in Column A is 2, while the slope in Column B is 3/2. Since 3/2 is greater than 2, the quantity in Column B is greater.
Therefore, the answer to question 15 is: b. The quantity in Column B is greater.
3. Simplifying (0.5(2.3 + 25))/1.5 to the nearest tenth:
To simplify this expression, follow the order of operations (PEMDAS/BODMAS). Start by evaluating the expression inside the parentheses first:
2.3 + 25 = 27.3
Now, substitute the simplified value back into the original expression:
(0.5(27.3))/1.5
Next, perform the multiplication:
0.5 * 27.3 = 13.65
Finally, divide by 1.5:
13.65/1.5 = 9.1
Therefore, simplifying (0.5(2.3 + 25))/1.5 to the nearest tenth gives you the answer 9.1.
I hope this explanation helps you understand and verify your answers!