Studdy AI Logo
Math  /  Algebra

QuestionFor each equation, choose the statement that describes its solution If applicable, give the solution. −2(y+1)+5y=3(y+1)−2-2(y+1)+5 y=3(y+1)-2 No solution y=y= □\square All real numbers are solutions 4(w+2)−w=2(w−1)+94(w+2)-w=2(w-1)+9 No solution w=w= □\square All real numbers are solutions Check

Studdy Solution

STEP 1

1. We are given two separate equations to solve.
2. We need to determine if each equation has no solution, a specific solution, or if all real numbers are solutions.

STEP 2

1. Solve the first equation for y y .
2. Analyze the solution for the first equation.
3. Solve the second equation for w w .
4. Analyze the solution for the second equation.

STEP 3

Start with the first equation: −2(y+1)+5y=3(y+1)−2 -2(y+1) + 5y = 3(y+1) - 2
Distribute the terms: −2y−2+5y=3y+3−2 -2y - 2 + 5y = 3y + 3 - 2
Combine like terms: 3y−2=3y+1 3y - 2 = 3y + 1

STEP 4

Subtract 3y 3y from both sides: 3y−2−3y=3y+1−3y 3y - 2 - 3y = 3y + 1 - 3y
Simplify: −2=1 -2 = 1
This is a contradiction, which means there is no solution.

STEP 5

The first equation has no solution.

STEP 6

Start with the second equation: 4(w+2)−w=2(w−1)+9 4(w+2) - w = 2(w-1) + 9
Distribute the terms: 4w+8−w=2w−2+9 4w + 8 - w = 2w - 2 + 9
Combine like terms: 3w+8=2w+7 3w + 8 = 2w + 7

STEP 7

Subtract 2w 2w from both sides: 3w−2w+8=2w−2w+7 3w - 2w + 8 = 2w - 2w + 7
Simplify: w+8=7 w + 8 = 7
Subtract 8 from both sides: w=7−8 w = 7 - 8
Simplify: w=−1 w = -1

STEP 8

The second equation has a specific solution: w=−1 w = -1 .
The solutions are:
1. First equation: No solution
2. Second equation: w=−1 w = -1

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord