Could someone check these questions for me? Please? My answers are under the questions...
Questions~
1. Solve:
| x | = 6
|6|=6 and |-6|=6
x must be 6 or -6
2. Solve:
| x + 7 | = 12
(x+7)=12 and -(x+7)=12
x+7=12 and -x-7=12
x= 5 and -19=x
The the solution is x = {–19, 5}
3. Solve:
| 3x - 4 | = 32
(3x-4)=32 and -(3x-4)=23
3x+4=32 and -3x+4=32
X=12 and x= -28/3
the solution is x = {-28/3, 12}
4. Solve:
5|2x + 1 | = 55
Divide both side by 5: |2x+1|=6.111111111111111
2x+1=6.111111111111111
+1 +1
2x = 7.11111111111
X=7
and
2x+1= -6.111111111111111
+1 +1
2x = -5.11111111111 x=-6
the solution is x = {-6, 7}
These questions I couldn't figure out could you please show me how to do them?
5. Solve:
1/2|4x – 8| - 7 = 3
6. Evaluate the given expressions when a = 3, b = -3, c = 4, and d = -1.
c|a-b| + d
7. Evaluate the given expressions when a = 3, b = -3, c = 4, and d = -1.
a|b-d| + ad
8. Evaluate the given expressions when a = 3, b = -3, c = 4, and d = -1
(a/c)|c| + b – d
#1, #2 ok
#3
your connective should be OR
how can a number be 12 and -28/3
#4
5|2x + 1 | = 55
|2x + 1 | = 11
2x+1 = 11 OR -2x-1 = 11
2x = 10 or -2x = 12
x = 5 or x = -6
5. Solve:
1/2|4x – 8| - 7 = 3
5. Solve:
1/2|4x – 8| = 10
5. Solve:
|4x – 8| = 20
4x-8 = 20 or -4x + 8 = 20
x = 7 or x = -3
a = 3, b = -3, c = 4, and d = -1
#6
c|a-b| + d
= -1|3 - (-3)|
= -1|6) = -6
#7
a|b-d| + ad
= 3|-3-(-1)| + 3(-1)
= 3(2) - 3
= 3
You do the last one in the same way
okay! Thank you so much!!
Sure! Let's go through the questions one by one.
5. Solve: 1/2|4x – 8| - 7 = 3
To solve this equation, we need to isolate the absolute value expression. Let's start by adding 7 to both sides of the equation:
1/2|4x – 8| = 10
Next, we can eliminate the fraction by multiplying both sides of the equation by 2:
|4x – 8| = 20
Now, we have an absolute value equation. To solve it, we can split it into two cases:
Case 1: 4x - 8 = 20
Solving this equation, we add 8 to both sides:
4x = 28
Dividing both sides by 4:
x = 7
Case 2: -(4x - 8) = 20
Solving this equation, we distribute the negative sign:
-4x + 8 = 20
Subtracting 8 from both sides:
-4x = 12
Dividing both sides by -4:
x = -3
Therefore, the solutions to the equation are x = 7 and x = -3.
6. Evaluate the given expressions when a = 3, b = -3, c = 4, and d = -1. c|a-b| + d
To evaluate this expression, we substitute the given values into the expression:
c|a-b| + d = 4|3-(-3)| + (-1)
Simplifying, we have:
4|6| - 1
Since the absolute value of 6 is 6, we have:
4 * 6 - 1 = 24 - 1 = 23
So, when a = 3, b = -3, c = 4, and d = -1, the expression evaluates to 23.
7. Evaluate the given expressions when a = 3, b = -3, c = 4, and d = -1. a|b-d| + ad
Similarly, we substitute the given values into the expression:
a|b-d| + ad = 3|-3-(-1)| + 3*(-1)
Simplifying, we have:
3| -3 + 1| - 3
Since -3 + 1 = -2, we have:
3| -2| - 3
Since the absolute value of -2 is 2, we have:
3 * 2 - 3 = 6 - 3 = 3
So, when a = 3, b = -3, c = 4, and d = -1, the expression evaluates to 3.
8. Evaluate the given expressions when a = 3, b = -3, c = 4, and d = -1. (a/c)|c| + b – d
Again, we substitute the given values into the expression:
(a/c)|c| + b – d = (3/4)|4| + (-3) - (-1)
Simplifying, we have:
(3/4)*4 + (-3) + 1
Cancelling out the multiplication, we have:
3 + (-3) + 1 = 1
So, when a = 3, b = -3, c = 4, and d = -1, the expression evaluates to 1.
I hope this helps! Let me know if you have any more questions.