Which step is missing when solving the equation for x?
8x + 4 = 6 - 2(x - 4)
8x + 4 = 6 - 2x + 8
10x + 4 = 14
10x = 10
x = 1
A. 8x + 4 = 12x
B. 8x + 4 = 14 - 2x
C. 8x = -2x +10
D. -12 = -12x
The missing step is option B: 8x + 4 = 14 - 2x.
The missing step when solving the equation 8x + 4 = 6 - 2(x - 4) is rewriting the equation after distributing the -2 to the terms inside the parentheses. So, the missing step is:
B. 8x + 4 = 14 - 2x
To solve the equation for x, we need to simplify both sides of the equation and isolate the variable.
Let's go step by step:
1. Start with the given equation: 8x + 4 = 6 - 2(x - 4).
2. Distribute the -2 to both terms inside the parentheses:
8x + 4 = 6 - 2x + 8.
3. Combine the like terms on the right side of the equation:
8x + 4 = 14 - 2x.
4. Simplify the equation further by adding 2x to both sides to get rid of the -2x:
8x + 2x + 4 = 14.
Now we have: 10x + 4 = 14.
5. Lastly, subtract 4 from both sides to isolate the variable:
10x = 14 - 4,
which simplifies to: 10x = 10.
6. Finally, divide both sides by 10 to solve for x:
x = 10 / 10,
which gives us the solution: x = 1.
Now let's review the provided options to identify the missing step:
A. 8x + 4 = 12x: This is the original equation, not a missing step.
B. 8x + 4 = 14 - 2x: This is the equation after distributing the -2 as shown in step 2 above.
C. 8x = -2x + 10: This is not a valid equation resulting from the steps given.
D. -12 = -12x: This equation is not related to the given equation at all.
Therefore, the missing step is:
B. 8x + 4 = 14 - 2x.