Help pllsss ASAP!!!
have certain answers!! i try but i do not understand! help asap! give answers and walkthrough problems for me!
1. 2(x - 3) = 2x (1 point)
one solution
no solutions
infinitely many solutions
2. 3(y - 3) = 2y - 9 + y (1 point)
one solution
no solutions
infinitely many solutions
3. 10x - 2 - 6x = 3x - 2 + x
one solution
no solutions
infinitely many solutions
4. 4(x +3) + 2x = x - 8
one solution
no solutions
infinitely many solutions
Thank you!!
B
C
C
A
100%
Trust me
B
C
C
A!
Anonymous is correct!!!!!!!!!!!!!!!!!!!!
1.
2 ( x - 3 ) = 2 x
2 * x - 2 * 3 = 2 x
2 x - 6 = 2 x subtract 2 x to both sides
2 x - 6 - 2 x = 2 x - 2 x
- 6 = 0
False.
No solutions
2.
3 ( y - 3 ) = 2 y - 9 + y
3 * y - 3 * 3 = 2 y - 9 + y
3 y - 9 = 3 y - 9
True for all values of y.
infinitely many solutions
3.
10 x - 2 - 6 x = 3 x - 2 + x
10 x - 6 x - 2 = 3 x + x - 2
4 x - 2 = 4 x - 2
True for all values of x.
infinitely many solutions
4.
4 ( x + 3 ) + 2 x = x - 8
4 * x + 4 * 3 + 2 x = x - 8
4 x + 12 + 2 x = x - 8
6 x + 12 = x - 8 Subtract x to both sides
6 x + 12 - x = x - 8 - x
5 x + 12 = - 8 Subtract 12 to both sides
5 x + 12 - 12 = - 8 - 12
5 x = - 20 Divide both sides by 5
5 x / 5 = - 20 / 5
x = - 4
one solution
If you end up with
some x equals something, then there will be one solution
e.g. #4
4(x+3)+2x = x-8
4x + 12 + 2x = x-8
5x = -20 ----> some x equals something
x = -4 -----> one solution
if your x term drops out, and you end up with a true statement, there will be an infinite number of solutions
if your x drops out, but you end up with a False statement, there is no solution.
e.g. #2
3(y-9) = 2y - 9 + y
3y - 27 = 3y - 9
-27 = -9 , what do you think, is it true or false ??
do the others the same way
Thank you sooooo much guys!!! Got 100%!
I'm here to help! Let's solve these problems step by step.
1. 2(x - 3) = 2x
To solve this equation, we need to distribute the 2 on the left side of the equation:
2x - 6 = 2x
Now, we can see that 2x is present on both sides of the equation. Let's subtract 2x from both sides to isolate the variable:
-6 = 0
Uh-oh! We end up with a contradiction - the equation -6 = 0 is false. This means there are no solutions to this equation. Hence, the answer is "no solutions."
2. 3(y - 3) = 2y - 9 + y
Let's distribute the 3 on the left side:
3y - 9 = 2y - 9 + y
Now, let's combine like terms on both sides of the equation:
3y - 9 = 3y - 9
Notice that we have the same term on both sides, so when we subtract 3y from both sides, it cancels out:
-9 = -9
This equation is true! It means that any value for y will satisfy this equation. Therefore, there are infinitely many solutions.
3. 10x - 2 - 6x = 3x - 2 + x
First, let's combine like terms on both sides:
4x - 2 = 4x - 2
Now, subtracting 4x from both sides cancels out the terms with x:
-2 = -2
This equation is true! It means that any value for x will satisfy this equation. Therefore, there are infinitely many solutions.
4. 4(x + 3) + 2x = x - 8
Let's simplify the left side by distributing the 4:
4x + 12 + 2x = x - 8
Combining like terms:
6x + 12 = x - 8
Now, let's isolate the variable on one side and the constant term on the other side:
6x - x = -8 - 12
5x = -20
Finally, let's solve for x by dividing both sides by 5:
x = -20/5
Simplifying the right side:
x = -4
We found a unique solution for x, so the answer is "one solution."
I hope this helps you understand how to approach and solve these types of problems! If you have any further questions, feel free to ask.