Multi-Step Equations
Solving Equations with Variables on Both Sides
1) 5y + 4 = 4y + 5
11a + 9 = 4a + 30
2w + 3 = 4w - 5
2) 3a - 10 = 4 + a
2x - 1 = x - 3
6n + 4 = n - 11
3) 29r + 4 = 28 + 13r
7x - 11 = -19 + 3x
4) b + 3 = 2b - 7
I'm having a bit trouble and really confused with the problems. I'm NOT asking you to do this homework for me because that would wrong and I won't learn anything. Can you do #1, 2, 3, and 4 for me for I can do the problems below it since it's similar to them.
You're welcome.
Your answer is correct.
2x - x = 3 - 1
1x = 2/1
x = 2
Yes.
1)
5y + 4 = 4y + 5
5y - 4y = 5 - 4
y = 1
2)
3a - 10 = 4 + a
3a - a = 4 + 10
2a = 14
a = 2
3)
29r + 4 = 28 + 13r
29r - 13r = 28 - 4
16r = 24
r = 24/16 = 1 8/16 = 1 1/2
thanks
2w + 3 = 4w - 5
4w - 2w = 3 + 5
2w = 8/2
w = 4
am i correct????
Of course! I'll guide you through solving each of the equations step-by-step so that you can understand the process. Remember, the goal is to isolate the variable on one side of the equation.
Let's start with the first set of equations:
1) 5y + 4 = 4y + 5
To solve this equation, we want to get all the terms with y on one side and the constant terms on the other side. Here's how you can do it:
Step 1: Start by subtracting 4y from both sides to move all the y terms to the left side of the equation:
5y + 4 - 4y = 4y + 5 - 4y
This simplifies to:
y + 4 = 5
Step 2: Next, subtract 4 from both sides to isolate the y term:
y + 4 - 4 = 5 - 4
y = 1
So the solution to the equation 5y + 4 = 4y + 5 is y = 1.
Now let's move on to the second equation:
2) 3a - 10 = 4 + a
Step 1: Start by subtracting a from both sides:
3a - a - 10 = 4 + a - a
This simplifies to:
2a - 10 = 4
Step 2: Next, add 10 to both sides to isolate the a term:
2a - 10 + 10 = 4 + 10
2a = 14
Step 3: Finally, divide both sides by 2 to solve for a:
2a/2 = 14/2
a = 7
So the solution to the equation 3a - 10 = 4 + a is a = 7.
Moving on to the third equation:
3) 29r + 4 = 28 + 13r
Step 1: Start by subtracting 13r from both sides:
29r - 13r + 4 = 28 + 13r - 13r
This simplifies to:
16r + 4 = 28
Step 2: Next, subtract 4 from both sides to isolate the r term:
16r + 4 - 4 = 28 - 4
16r = 24
Step 3: Finally, divide both sides by 16 to solve for r:
16r/16 = 24/16
r = 3/2
So the solution to the equation 29r + 4 = 28 + 13r is r = 3/2.
Now, let's move to the last equation:
4) b + 3 = 2b - 7
Step 1: Start by subtracting b from both sides:
b - b + 3 = 2b - b - 7
This simplifies to:
3 = b - 7
Step 2: Next, add 7 to both sides to isolate the b term:
3 + 7 = b - 7 + 7
10 = b
So the solution to the equation b + 3 = 2b - 7 is b = 10.
I hope this explanation helps you understand how to solve multi-step equations with variables on both sides. Let me know if you have any further questions!