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Math  /  Algebra

Question5y−3−3y=3y+5−3y5 y-3-3 y=3 y+5-3 y

Studdy Solution

STEP 1

1. The equation 5y−3−3y=3y+5−3y5y - 3 - 3y = 3y + 5 - 3y is a linear equation.
2. We need to solve for the variable yy.
3. The equation involves combining like terms and basic algebraic operations.

STEP 2

1. Simplify both sides of the equation by combining like terms.
2. Isolate the variable yy on one side of the equation.
3. Verify the solution by substituting it back into the original equation.

STEP 3

Simplify the left-hand side of the equation by combining like terms:
5y−3y−3=(5y−3y)−3=2y−3 5y - 3y - 3 = (5y - 3y) - 3 = 2y - 3

STEP 4

Simplify the right-hand side of the equation by combining like terms:
3y−3y+5=(3y−3y)+5=0+5=5 3y - 3y + 5 = (3y - 3y) + 5 = 0 + 5 = 5

STEP 5

Now, the equation is simplified to:
2y−3=5 2y - 3 = 5
Add 3 to both sides to isolate the term with yy:
2y−3+3=5+3 2y - 3 + 3 = 5 + 3
2y=8 2y = 8

STEP 6

Divide both sides by 2 to solve for yy:
2y2=82 \frac{2y}{2} = \frac{8}{2}
y=4 y = 4

STEP 7

Verify the solution by substituting y=4y = 4 back into the original equation:
Left-hand side:
5(4)−3−3(4)=20−3−12=5 5(4) - 3 - 3(4) = 20 - 3 - 12 = 5
Right-hand side:
3(4)+5−3(4)=12+5−12=5 3(4) + 5 - 3(4) = 12 + 5 - 12 = 5
Both sides are equal, confirming the solution is correct.
The solution is:
4 \boxed{4}

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