Question

What is the value of n in the equation –negative StartFraction one-half EndFraction left-parenthesis 2 n plus 4 right-parenthesis plus 6 equals negative 9 plus 4 left parenthesis 2 n plus 1 right-parenthesis.(2n + 4) + 6 = –9 + 4(2n + 1)?

n =

Answer 1

To solve the equation, distribute and simplify both sides, then isolate the variable 'n'. The value of 'n' is 1.

Step-by-step explanation:

To solve the equation, we need to simplify both sides and isolate the variable 'n'.

Starting with the left side of the equation:

1. Distribute the negative sign: -1/2(2n + 4) + 6
2. Multiply: -n - 2 + 6
3. Combine like terms: -n + 4

Now let's simplify the right side of the equation:

1. Distribute the 4: -9 + 4(2n + 1)
2. Multiply: -9 + 8n + 4
3. Combine like terms: 8n - 5

Setting the simplified left side equal to the simplified right side:

-n + 4 = 8n - 5

Now we can solve for 'n':

1. Add 'n' to both sides: 4 = 9n - 5
2. Add 5 to both sides: 9 = 9n
3. Divide both sides by 9: n = 1