Answer: y = 3.2
Explanation:
To solve the equation 2y − 2.3 = 4.1 for y, we can use algebraic manipulation.
Step 1:
In order to remove the constant term on the left-hand side of the equation, we first add 2.3 to both sides of the equation:
2y - 2.3 = 4.1
+2.3 +2.3
2y = 6.4
Step 2:
Now, we divide both sides by 2 to isolate y:
2y = 6.4
÷2 ÷2
y = 3.2
So, the solution to this equation is y = 3.2
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Summary
We need to isolate the variable on one side of the equation in order to solve an equation like this. By carrying out the same method on both sides of the equation, we can do this. In this example, we divided both sides by 2 to isolate y after adding 2.3 to both sides to remove the constant term on the left-hand side.
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FAQ
What is a constant term?
- A term in an algebraic equation that has no variables and is steady is known as a constant term in mathematics. A constant is a fixed, unchanging value. A constant in algebra can be a number on its own or sometimes a letter like a, b, or c to show a fixed integer.
What isolating y mean, in this case?
- To separate y from all other terms in an equation, the equation must be rewritten so that y is on one side and all other terms are on the other side. It allows us to calculate the value of y and solve for it.
What is algebraic manipulation?
- Mathematical operations including addition, subtraction, multiplication, and division are used to rearrange algebraic expressions or equations to try to simplify or solve them. This process is known as algebraic manipulation. By doing the opposite operations (undoing) to any equation, algebraic manipulation tries to isolate a variable or simplify an expression in order to solve for a certain variable.