Question
Solve using the principles together. Check your answer. \[ 7 y-4=35-6 y \] The solution is \( y=\square \). (Type an integer or a simplified fraction.)
Ask by Rojas Jimenez. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( y = 3 \).
Solution
We start with the equation:
7y − 4 = 35 − 6y
Step 1. Add 6y to both sides to get all y terms on one side:
7y + 6y − 4 = 35
13y − 4 = 35
Step 2. Add 4 to both sides to isolate the y term:
13y = 35 + 4
13y = 39
Step 3. Divide by 13:
y = 39 / 13
y = 3
Checking the answer by plugging y = 3 into the original equation:
Left-hand side: 7(3) − 4 = 21 − 4 = 17
Right-hand side: 35 − 6(3) = 35 − 18 = 17
Since both sides are equal, the solution is correct.
The solution is y = 3.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To solve the equation \( 7y - 4 = 35 - 6y \), we first want to get all the terms involving \( y \) on one side and constant terms on the other. 1. Add \( 6y \) to both sides: \[ 7y + 6y - 4 = 35 \] \[ 13y - 4 = 35 \] 2. Next, add 4 to both sides: \[ 13y = 35 + 4 \] \[ 13y = 39 \] 3. Finally, divide both sides by 13: \[ y = \frac{39}{13} \] \[ y = 3 \] So the solution is \( y = 3 \). Now let's check our answer by substituting \( y = 3 \) back into the original equation: Left side: \[ 7(3) - 4 = 21 - 4 = 17 \] Right side: \[ 35 - 6(3) = 35 - 18 = 17 \] Since both sides equal 17, the solution \( y = 3 \) is correct!
