A student is solving the equation 81x – 1 = 3x + 2.
Step 1: 81x – 1 = 3x + 2
Step 2: (34)x – 1 = 3x + 2
Step 3: 34x – 4 = 3x + 2
Which is the next step?
Possible answers
4x 4 = (x + 2)
x 1 = x + 2
4x 4 = x + 2
4(x 1) = 3(x + 2)
How do you get from step 1 to step 2? Do you have some typos?
Subtract 3x and add 1 to both sides of the equation.
To find the next step in solving the equation 81x – 1 = 3x + 2, we need to simplify the equation by combining like terms on both sides. Let's look at the given options:
1. 4x - 4 = (x + 2)
2. x - 1 = x + 2
3. 4x - 4 = x + 2
4. 4(x - 1) = 3(x + 2)
Among these options, the correct next step is option 4: 4(x - 1) = 3(x + 2).
Explanation:
To simplify the equation, we need to distribute the numbers in the parentheses. Distributing the 4 on the left side gives us 4x - 4, and distributing the 3 on the right side gives us 3x + 6. Thus, the equation becomes:
4(x - 1) = 3(x + 2)
Now we have a simpler equation that we can solve further to find the value of x.