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Math  /  Algebra

QuestionSolve 4(y+2)−3=−y4(y+2)-3=-y. y=y=

Studdy Solution

STEP 1

1. The equation 4(y+2)−3=−y 4(y+2) - 3 = -y is a linear equation in one variable, y y .
2. The goal is to isolate y y on one side of the equation.
3. The equation involves distributing, combining like terms, and solving for y y .

STEP 2

1. Distribute the 4 across the terms inside the parentheses.
2. Combine like terms on the left side of the equation.
3. Move all terms involving y y to one side of the equation.
4. Solve for y y .
5. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the 4 across the terms inside the parentheses:
4(y+2)=4y+8 4(y+2) = 4y + 8
So, the equation becomes:
4y+8−3=−y 4y + 8 - 3 = -y

STEP 4

Combine like terms on the left side of the equation:
4y+8−3=4y+5 4y + 8 - 3 = 4y + 5
So, the equation now is:
4y+5=−y 4y + 5 = -y

STEP 5

Move all terms involving y y to one side of the equation. Add y y to both sides:
4y+y+5=−y+y 4y + y + 5 = -y + y
This simplifies to:
5y+5=0 5y + 5 = 0

STEP 6

Isolate y y by subtracting 5 from both sides:
5y+5−5=0−5 5y + 5 - 5 = 0 - 5
This simplifies to:
5y=−5 5y = -5
Divide both sides by 5 to solve for y y :
y=−55 y = \frac{-5}{5}
y=−1 y = -1

STEP 7

Check the solution by substituting y=−1 y = -1 back into the original equation:
Original equation: 4(y+2)−3=−y 4(y+2) - 3 = -y
Substitute y=−1 y = -1 :
4((−1)+2)−3=−(−1) 4((-1)+2) - 3 = -(-1)
Simplify both sides:
4(1)−3=1 4(1) - 3 = 1
4−3=1 4 - 3 = 1
1=1 1 = 1
Both sides are equal, confirming the solution is correct.
The solution is:
−1 \boxed{-1}

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