What Is The Value Of N In The Equation (n – 4) – 3 = 3 – (2n + 3)? n =
When it comes to solving equations, sometimes we encounter complex expressions that require careful steps to find the value of the variable. In this particular case, we are faced with the equation (n – 4) – 3 = 3 – (2n + 3), and our goal is to determine the value of n. Let’s break down the steps to solve this equation.
The first step is to simplify both sides of the equation by removing any parentheses or brackets. By applying the distributive property, we can rewrite the right side as 3 – 2n – 3. This simplifies further to -2n.
Next, we combine like terms on each side of the equation. On the left side, combining -4 and -3 gives us -7. So now we have n – 7 = -2n.
To isolate n on one side of the equation, we need to get rid of the terms containing n on both sides. We do this by adding 2n to both sides, resulting in n + 2n -7 = -2n + 2n. Simplifying further gives us 3n -7 =0.
Finally, adding 7 to both sides of the equation will allow us to isolate n completely. Adding 7 results in:
(3n-7) +7 =0+7 Combining like terms gives: 3n=7
To find out what n equals, divide both sides by 3: (3/3)n=7/3 Simplifying further: 1 * n = (7/3)
Therefore, after following these steps diligently and systematically solving for n in our given equation (n –4)–3=3–(2𝑛+𝑛), we discover that 𝑛= (𝟕/𝟑).
Remember that practice makes perfect when it comes to solving equations. By mastering these steps, you’ll be able to confidently solve even more complex equations in the future.
Simplifying the Equation: Steps to Finding the Value of n
In order to find the value of n in the equation (n – 4) – 3 = 3 – (2n + 3), we need to simplify the equation. By following a few steps, we can make it easier to solve and determine the unknown value.
- Distribute and Combine Like Terms: Start by distributing any terms inside parentheses and combining like terms. In this equation, we have two sets of parentheses – one on each side. Let’s break it down step by step:
(n – 4) – 3 = 3 – (2n + 3)
First, distribute the negative sign inside the second set of parentheses:
(n – 4) – 3 = 3 – 2n – 3
Next, combine like terms on both sides of the equation:
n – 4 – 3 = 0 + n n -7 = n
- Move Variables to One Side: Now that we have simplified the equation, our next step is to move all variables to one side and constants to the other side. To do this, we’ll subtract ‘n’ from both sides:
-7 = n – n -7 =0
At this point, we see that ‘n’ cancels out completely and leaves us with a contradiction: ‘-7=0’. This means that there is no value for ‘n’ that satisfies this equation.
Therefore, after simplifying the given equation, we find that there is no solution for ‘n’ since it leads to a contradiction.
Combining Like Terms
Now that we have the equation (n – 4) – 3 = 3 – (2n + 3), let’s move on to the next step in solving for the value of n. This step is called “combining like terms”.
Combining like terms involves simplifying expressions by adding or subtracting terms that have the same variable and exponent. In our equation, we have two sets of like terms: n and -2n.
To begin, let’s simplify the left side of the equation. We have (n – 4) – 3. To combine these terms, we need to distribute the negative sign to both -4 and -3:
(n – 4) – 3 = n – 4 – 3 = n -7
On the right side of the equation, we have 3 – (2n + 3). Here, we need to distribute the negative sign to both terms inside the parentheses:
3 – (2n + 3) = 3 -2n – 3 = (-2n)
Now that we’ve simplified both sides of the equation, let’s combine them together:
n-7 = (-2n)
To isolate n on one side of the equation, we can add ‘2n’ to both sides:
(1+2)n-7 = (-2n)+(2n) => (1+2)n-7 =0
Simplifying further,
(1+2)n-7 =0 => (1+2)n-=-7
Finally, dividing both sides by ‘1+2’, we find:
(n)=-7/(1+(-(+))) Isolating the Variable
Now that we have the equation (n – 4) – 3 = 3 – (2n + 3), our next step is to isolate the variable, n. This means we need to rearrange the equation so that n is on one side of the equals sign and all other terms are on the other side.
To begin isolating the variable, let’s simplify both sides of the equation by performing any necessary operations. Starting with the left side, we can simplify (n – 4) – 3 as follows:
(n – 4) – 3 = n – (4 + 3) = n – 7
On the right side of the equation, let’s simplify 3 – (2n + 3):
3 – (2n + 3) = -1(2n + 3) + 3 = -2n – 6 + 3 = -2n – 3
Now that we have simplified both sides of the equation, our new equation is:
n -7 = -(2n+3)
