Please help me! Sorry there are 4 questions I need to check my attempts with to see if I am on track. Thanks!!
1. 5-3[2(3x-4)+3]
2. Evaluate when x = -3 and y = 2
3x squared - 4y squared
_______________________
4x - 7y
3. -3/4y = -24
4. m + 1 + 5 = 2m - 1
______ _ _______
4 6 = 12
Sure, I can help you with your questions! Let's go through each of them step by step.
1. 5 - 3[2(3x-4)+3]
To simplify this expression, we need to follow the order of operations (also known as PEMDAS).
First, let's simplify the expression inside the innermost parentheses:
2(3x - 4) + 3 = 6x - 8 + 3 = 6x - 5
Now, substitute the simplified expression back into the original equation:
5 - 3(6x - 5)
Next, distribute the -3 to both terms inside the parentheses:
5 - (18x - 15)
When we distribute the negative sign, it changes the sign of each term inside the parentheses:
5 - 18x + 15
Combine like terms:
(5 + 15) - 18x = 20 - 18x
So, the simplified expression is 20 - 18x.
2. To evaluate the expression when x = -3 and y = 2:
Substitute x = -3 and y = 2 into the expression:
3x^2 - 4y^2
_____________
4x - 7y
First, calculate the values of the variables:
3(-3)^2 - 4(2)^2
_____________
4(-3) - 7(2)
Simplify the expression:
3(9) - 4(4)
___________
-12 - 14
Calculate the values inside the parentheses:
27 - 16
_______
-26
Subtract and simplify:
11
_____
-26
So, the value of the expression when x = -3 and y = 2 is -11/26.
3. To solve the equation -3/4y = -24:
Multiply both sides of the equation by 4 to get rid of the fraction:
4 * (-3/4y) = 4 * (-24)
Simplify:
-3y = -96
Divide both sides of the equation by -3 to solve for y:
-3y / -3 = -96 / -3
Simplify:
y = 32
So, the solution to the equation -3/4y = -24 is y = 32.
4. To solve the equation m + 1 + 5 = 2m - 1:
Combine like terms on both sides of the equation:
m + 6 = 2m - 1
Subtract m from both sides to isolate the variable on one side:
m - m + 6 = 2m - 1 - m
Simplify:
6 = m - 1
Add 1 to both sides of the equation to solve for m:
6 + 1 = m - 1 + 1
Simplify:
7 = m
So, the solution to the equation m + 1 + 5 = 2m - 1 is m = 7.
I hope this helps! Let me know if you have any further questions.