14. Describe the number of solutions for the equation
-2(y-3) =2y-6
a. one solution
b. no solution
c. infinite solutions
my answer is c. i have a few more questions for this test and if anyone could help me that would be great.
- 2 ( y - 3 ) = 2 y - 6
- 2 ∙ y - 2 ∙ ( - 3 ) = 2 y - 6
- 2 y + 6 = 2 y - 6
Subtract 2 y to both sides
- 2 y + 6 - 2 y = 2 y - 6 - 2 y
- 4 y + 6 = - 6
Subtract 6 to both sides
- 4 y + 6 - 6 = - 6 - 6
- 4 y = - 12
Divide both sides by - 4
y = - 12 / - 4
y = 3
a. one solution
Well, solving equations can be a tricky business, but luckily I'm here to help and add a touch of humor! So, let's solve this equation together.
-2(y-3) = 2y-6
First, let's distribute the -2 to the terms inside the parentheses:
-2y + 6 = 2y - 6
Now, let's gather all the y terms on one side by adding 2y to both sides and subtracting 6 from both sides:
6 + 6 = 2y + 2y
12 = 4y
Next, let's divide both sides of the equation by 4:
12/4 = 4y/4
3 = y
So, the solution to the equation is y = 3.
And since we have found a unique value for y, the answer is a. one solution!
Remember, if you have any more questions, I'm here to help and make you smile along the way!
To determine the number of solutions for the equation -2(y-3) =2y-6, we can simplify it step by step:
Step 1: Distribute the -2 on the left side:
-2y + 6 = 2y - 6
Step 2: Move the terms with -2y and 2y to the same side:
-2y - 2y = -6 - 6
-4y = -12
Step 3: Divide both sides by -4 to solve for y:
y = -12 / -4
y = 3
Now, let's substitute the value of y back into the original equation to verify if it holds:
-2(y-3) = 2y - 6
-2(3-3) = 2(3) - 6
-2(0) = 6 - 6
0 = 0
The equation is true, indicating that the value of y = 3 is a valid solution.
Therefore, the number of solutions for the equation -2(y-3) = 2y-6 is a. one solution.
To determine the number of solutions for the equation -2(y-3) = 2y-6, we can simplify the equation and then analyze it.
First, let's simplify the left side of the equation by distributing the -2:
-2(y-3) = 2y-6
-2y + 6 = 2y - 6
Next, let's gather all the y terms on one side and all the constant terms on the other side:
-2y - 2y = -6 - 6 - 2
-4y = -14
Now, divide both sides of the equation by -4:
(-4y)/(-4) = (-14)/(-4)
y = 14/4
y = 7/2
So, we have found a single solution for the equation, which means the answer is:
a. one solution
If you have more questions, feel free to ask, and I'll do my best to help you!