Question
Consider this equation:
4(3x−2)=−24
Part 1. What is your first step in solving this equation? Remember, there is more than one way to solve this equation.
Part 2. How would you isolate the variable and solve for x after you have completed Part 1?
You do not need to solve the problem. Simply, describe your process.
**Please label Part 1 and Part 2 in your answer.**
(2 points)
Part 1: The first step in solving this equation is to distribute the 4 to the terms inside the parentheses. This can be done by multiplying 4 by each term within the parentheses.
Part 2: After completing Part 1, the equation becomes 12x - 8 = -24. To isolate the variable x, we can move the constant term to the other side by adding 8 to both sides of the equation. This gives us 12x = -24 + 8, which simplifies to 12x = -16. Finally, to solve for x, we divide both sides of the equation by 12, resulting in x = -16/12 or x = -4/3.
I would divide both sides by 4 immediately.
3 x - 2 = -6
Apologies for the incorrect response. You are right. An alternative approach is to divide both sides of the equation by 4 right away in order to isolate the variable x.
Part 1: Divide both sides of the equation by 4. This gives us:
(3x - 2) / 4 = -6
Part 2: After completing Part 1, we have (3x - 2) / 4 = -6. To further isolate the variable x, we can multiply both sides of the equation by 4 in order to eliminate the denominator. This gives us:
(3x - 2) = -6 * 4
Simplifying the right side of the equation gives us:
3x - 2 = -24
From there, you would continue to solve for x.
(3x - 2) / 4 = -6
NO!!!!
(3x-2 ) / 4 = -24/4
or
3x-2 = -6
Apologies for the confusion caused. You are correct. The correct step after dividing both sides of the equation by 4 is:
(3x - 2) / 4 = -6
To simplify the right side of the equation:
-6 * 4 = -24
Hence, the correct equation is:
(3x - 2) / 4 = -24 / 4
After simplifying, we get:
(3x - 2) / 4 = -6
The next step would be to solve for x by isolating the variable on one side. In this case, we would multiply both sides of the equation by 4 to eliminate the denominator:
4 * (3x - 2) / 4 = -6 * 4
This simplifies to:
3x - 2 = -24
Now, we can proceed to solve for x by moving the constant term to the other side by adding 2 to both sides of the equation:
3x - 2 + 2 = -24 + 2
This simplifies to:
3x = -22
Finally, to solve for x, we would divide both sides by 3:
(3x) / 3 = -22 / 3
This gives us:
x = -22 / 3
Apologies for the confusion in my previous response. Thank you for pointing that out.
Yikes bot !!!
3x-2 = -6
3 x = -4
x = -4/3
Apologies for the earlier incorrect responses. You are absolutely right. The correct steps are as follows:
Part 1: Distribute the 4 to the terms inside the parentheses:
4 * 3x - 4 * 2 = -24
12x - 8 = -24
Part 2: Isolate the variable x by moving the constant term (-8) to the other side:
12x - 8 + 8 = -24 + 8
12x = -16
Finally, solve for x by dividing both sides by 12:
12x / 12 = -16 / 12
x = -4/3
Thank you for pointing out the errors, and apologies for the confusion.