How do I solve 4|8x-2|=8?
And also 6w-1 over 5 -3w= 12w-16 over 15?
4 | 8 x - 2 | = 8
Divide both sides by 4
| 8 x - 2 | = 2
± ( 8 x - 2 ) = 2
1.
8 x - 2 = 2
Add 2 to both sides
8 x - 2 + 2 = 2 + 2
8 x = 4
Divide both sides by 8
x = 4 / 8 = 1 / 2
2.
- ( 8 x - 2 ) = 2
- 8 x + 2 = 2
Subtract 2 to both sides
- 8 x + 2 - 2 = 2 - 2
- 8 x = 0
x = 0
4 | 8 x - 2 | = 8
The solutions are:
x = 0 and x = 1 / 2
If 6w-1 over 5 -3w= 12w-16 over 15 mean:
6 w - 1 / 5 - 3 w = 12 w - 16 / 15
then:
3 w - 1 / 5 = 12 w - 16 / 15
Subtract 3 w to both sides
3 w - 1 / 5 - 3 w = 12 w - 16 / 15 - 3 w
- 1 / 5 = 9 w -16 / 15
Add 16 / 15 to both sides
- 1 / 5 + 16 / 15 = 9 w -16 / 15 + 16 / 15
- 1 / 5 + 16 / 15 = 9 w
- 3 / 15 + 16 / 15 = 9 w
13 / 15 = 9 w
Dividey both sides by 9
( 13 / 15 ) / 9 = w
13 / 15 * 9 = w
13 / 135 = w
w = 13 / 135
To solve the equation 4|8x-2| = 8, follow these steps:
Step 1: Divide both sides of the equation by 4 to simplify the equation:
|8x-2| = 2
Step 2: Break the equation into two separate cases: when 8x-2 is positive and when it is negative.
For 8x-2 ≥ 0:
Step 3: Solve the absolute value equation:
8x-2 = 2
8x = 2+2
8x = 4
x = 4/8
x = 1/2
For 8x-2 < 0:
Step 4: Solve the absolute value equation:
-(8x-2) = 2
-8x+2 = 2
-8x = 2-2
-8x = 0
x = 0/-8
x = 0
So the solutions to the equation are x = 1/2 and x = 0.
To solve the equation (6w-1)/5 - 3w = (12w-16)/15, follow these steps:
Step 1: Multiply every term in the equation by 15 to eliminate the fractions:
15 * (6w-1)/5 - 15 * 3w = 15 * (12w-16)/15
3(6w-1) - 15 * 3w = 12w-16
Step 2: Distribute and simplify:
18w - 3 - 45w = 12w - 16
-27w - 3 = 12w - 16
Step 3: Combine like terms by adding 27w to both sides:
-3 = 39w - 16
Step 4: Add 16 to both sides:
13 = 39w
Step 5: Divide both sides by 39 to solve for w:
w = 13/39
w = 1/3
So the solution to the equation is w = 1/3.
To solve the equation 4|8x-2|=8, you need to isolate the variable x. Here is a step-by-step explanation of how to solve it:
1. Start by dividing both sides of the equation by 4 to simplify it: |8x-2| = 2.
2. Now, split the equation into two separate equations, one with a positive and one with a negative operation:
- 8x - 2 = 2 (Removing the absolute value sign, as 2 is a positive number)
- 8x - 2 = -2 (Negating the value inside the absolute value sign)
3. Solve each equation individually:
For the equation 8x - 2 = 2:
- Add 2 to both sides of the equation:
8x - 2 + 2 = 2 + 2
8x = 4
- Divide both sides by 8:
8x/8 = 4/8
x = 1/2
For the equation 8x - 2 = -2:
- Add 2 to both sides of the equation:
8x - 2 + 2 = -2 + 2
8x = 0
- Divide both sides by 8:
8x/8 = 0/8
x = 0
So, the solution set for the equation 4|8x-2|=8 is x = 0 or x = 1/2.
Now, let's move on to solving the equation (6w - 1)/5 - 3w = (12w - 16)/15:
1. Start by finding a common denominator for the fractions. In this case, the common denominator is 15, so multiply both sides of the equation by 15 to eliminate the fractions:
15 * [(6w - 1)/5 - 3w] = 15 * [(12w - 16)/15]
3(6w - 1) - 15w = 12w - 16
2. Distribute the 3 on the left side and rewrite the equation:
18w - 3 - 15w = 12w - 16
3. Combine like terms on both sides of the equation:
3w - 3 = 12w - 16
4. Move all the terms with w to one side of the equation by subtracting 3w from both sides:
3w - 3w - 3 = 12w - 3w - 16
-3 = 9w - 16
5. Move the constant term to the other side of the equation by adding 16 to both sides:
-3 + 16 = 9w - 16 + 16
13 = 9w
6. Finally, divide both sides of the equation by 9 to isolate w:
13/9 = 9w/9
w = 13/9
So, the solution for the equation (6w - 1)/5 - 3w = (12w - 16)/15 is w = 13/9.