I am working on a review worksheet and there are 2 problems I can't remember how to do. Each question has 6 other questions, so helping me with these will remind me how to do the others! Thank you!!
1.2(x+5) = 1.6(2x+5)
and
Solve for y
a(y+c) = b(y-c)
Thank you again!
Jeffrey
These are just exercises using the distributive property. Clear parentheses to get started.
1.2(x+5) = 1.6(2x+5)
1.2x + 6.0 = 3.2x + 8.0
2.0x = -2.0
x = -1.0
Or, if you dislike decimals, multiply by 5 to start with:
6(x+5) = 8(2x+5)
6x+30 = 16x+40
10x = -10
x = -1
a(y+c) = b(y-c)
ay+ac = by-bc
ay-by = -bc-ac
y(a-b) = -c(b+a)
y = -c(b+a)/(a-b)
or, y = c * (b+a)/(b-a)
Got it!
Thank you Steve!
Of course, I'll be happy to help you with those problems!
1. Let's start with the first problem: 1.2(x+5) = 1.6(2x+5). To solve this equation, we need to simplify both sides of the equation and then solve for x.
Firstly, let's distribute the numbers to eliminate the parentheses:
1.2 * x + 1.2 * 5 = 1.6 * 2x + 1.6 * 5
After distributing, the equation becomes:
1.2x + 6 = 3.2x + 8
Next, let's collect like terms by moving all the terms with x to one side of the equation and the constant terms to the other side.
1.2x - 3.2x = 8 - 6
Subtract 3.2x from both sides:
-2x = 2
Now, we can solve for x by dividing both sides of the equation by -2:
x = 2 / -2
Simplifying the right side, we get:
x = -1
So, the solution to the equation is x = -1.
Now, let's move on to the second problem: Solve for y in a(y+c) = b(y-c).
First, we'll distribute the numbers to eliminate the parentheses:
ay + ac = by - bc
Next, let's gather all the terms with y on one side and the constant terms on the other side:
ay - by = -ac - bc
Factoring out y from the left side of the equation, we get:
y(a - b) = -ac - bc
Finally, we can solve for y by dividing both sides of the equation by (a - b):
y = (-ac - bc) / (a - b)
So, the solution for y is y = (-ac - bc) / (a - b).
I hope this helps you solve the other questions on your review worksheet too! Let me know if you have any further questions.