solve and put your answers into the blue boxes. if y color will appear! the picture will only appear per$0.5(-4.2x + 6.6) = -2.1x + n$$0.2(12x + 8) = 2.4x + n$$(-2x + 9) + (-5x - 3) = -7x + n$$(-5x - 8) + (-3x+ 1) = n + -7$$(9x + 6) + (-4x + -5) = n + 1$$24x - 8 = 2(12x - n)$$24x - 8 = 4(n - 2)$$24x - 8 = n(3x - 1)$$\frac{1}{3}(- 18x - 12)=n - 4$$1.27 - \frac{35}{100} = \frac{n}{100} + \frac{35}{100}$

Question

Accepted Answer

Let's solve each equation for $ n $ one by one:

### 1. $ 0.5(-4.2x + 6.6) = -2.1x + n $
## Step1: Distribute 0.5
$ 0.5 \times (-4.2x) + 0.5 \times 6.6 = -2.1x + n $
$ -2.1x + 3.3 = -2.1x + n $
## Step2: Subtract $-2.1x$ from both sides
$ 3.3 = n $
# Answer: $ n = 3.3 $

### 2. $ 0.2(12x + 8) = 2.4x + n $
## Step1: Distribute 0.2
$ 0.2 \times 12x + 0.2 \times 8 = 2.4x + n $
$ 2.4x + 1.6 = 2.4x + n $
## Step2: Subtract $2.4x$ from both sides
$ 1.6 = n $
# Answer: $ n = 1.6 $

### 3. $ (-2x + 9) + (-5x - 3) = -7x + n $
## Step1: Combine like terms on the left
$ (-2x - 5x) + (9 - 3) = -7x + n $
$ -7x + 6 = -7x + n $
## Step2: Subtract $-7x$ from both sides
$ 6 = n $
# Answer: $ n = 6 $

### 4. $ (-5x - 8) + (-3x + 1) = n + (-7x) $
## Step1: Combine like terms on the left
$ (-5x - 3x) + (-8 + 1) = n - 7x $
$ -8x - 7 = n - 7x $
Wait, let's re - check the original equation. The original equation is $ (-5x - 8)+(-3x + 1)=n + (-7x) $
Combine like terms on the left: $ (-5x-3x)+(-8 + 1)=-8x-7 $
So the equation is $ -8x-7=n - 7x $
Add $8x$ to both sides: $ -7=n + x $
Wait, maybe I made a mistake. Let's start over.
Original equation: $ (-5x - 8)+(-3x + 1)=n-7x $
Left side: $ -5x-3x-8 + 1=-8x-7 $
So $ -8x-7=n-7x $
Add $7x$ to both sides: $ -x - 7=n $
Wait, this seems different. Wait, maybe the original equation was written as $ (-5x - 8)+(-3x + 1)=n + (-7) $? If that's the case:
Left side: $ -5x-3x-8 + 1=-8x-7 $
Right side: $ n - 7 $
So $ -8x-7=n - 7 $
Add 7 to both sides: $ -8x=n $
No, the user's equation is $ (-5x - 8)+(-3x + 1)=n + -7 $
So $ -8x-7=n - 7 $
Add 7 to both sides: $ -8x=n $
This can't be right. Maybe there is a typo. But assuming the equation is $ (-5x - 8)+(-3x + 1)=n-7x $ is wrong. Let's assume the correct combination:
Wait, $ (-5x-8)+(-3x + 1)=-8x-7 $ and the right side is $ n-7x $
Then, $ -8x-7=n - 7x $
Bring all $x$ terms to one side: $ -8x + 7x=n + 7 $
$ -x=n + 7 $
$ n=-x - 7 $
This is a problem. Maybe the original equation was $ (-5x - 8)+(-3x + 1)=n-7 $ (without the $x$ on the right). Let's try that.
If $ (-5x - 8)+(-3x + 1)=n-7 $
Left side: $ -8x-7 $
So $ -8x-7=n - 7 $
Add 7 to both sides: $ -8x=n $
No, this is confusing. Maybe we should skip this for now or check again.

### 5. $ (9x + 6)+(-4x-5)=n + 1 $
## Step1: Combine like terms on the left
$ (9x-4x)+(6 - 5)=n + 1 $
$ 5x+1=n + 1 $
## Step2: Subtract 1 from both sides
$ 5x=n $
Wait, no:
Left side: $9x-4x + 6-5 = 5x + 1$
So $5x + 1=n + 1$
Subtract 1 from both sides: $5x=n$
This is not a constant. Maybe the original equation was $ (9x + 6)+(-4x-5)=n + 1$ (with a sign error). If it's $ (9x + 6)+(-4x + 5)=n + 1$, but no. Wait, $9x-4x=5x$, $6-5 = 1$, so $5x + 1=n + 1$, then $n = 5x$. This is strange. Maybe the equation is $ (9x + 6)+(-4x-5)=n + 1$ (solving for $n$ in terms of $x$)? But the other equations seem to have $n$ as a constant. Maybe there is a typo. Let's assume that the equation is $ (9x + 6)+(-4x-5)=n + 1$ and we made a mistake. Let's re - calculate:
$9x-4x=5x$, $6-5 = 1$, so $5x + 1=n + 1$, subtract 1: $5x=n$.

### 6. $ 24x - 8=2(12x - n) $
## Step1: Distribute 2 on the right
$ 24x - 8=24x-2n $
## Step2: Subtract $24x$ from both sides
$ -8=-2n $
## Step3: Divide both sides by - 2
$ n = 4 $
# Answer: $ n = 4 $

### 7. $ 24x - 8=4(n - 2) $
## Step1: Distribute 4 on the right
$ 24x - 8=4n-8 $
## Step2: Add 8 to both sides
$ 24x=4n $
## Step3: Divide both sides by 4
$ 6x=n $
Wait, this gives $n$ in terms of $x$. But maybe the equation is $24 - 8=4(n - 2)$ (without the $x$). If that's the case:
$16 = 4n-8$
Add 8: $24 = 4n$
$n = 6$
But the original equation has $24x-8 = 4(n - 2)$. So:
$24x-8=4n-8$
Add 8: $24x=4n$
Divide by 4: $6x=n$

### 8. $ 24x - 8=n(3x - 1) $
## Step1: Expand the right side
$ 24x - 8=3nx - n $
## Step2: Group like terms
For the coefficients of $x$ to be equal (assuming $n$ is a constant), $3n = 24$ (coefficient of $x$ on left is 24, on right is $3n$)
## Step3: Solve for $n$ from $3n = 24$
$n = 8$
Check the constant term: When $n = 8$, the right side constant term is $-n=-8$, and the left side constant term is - 8. So it works.
# Answer: $ n = 8 $

### 9. $ \frac{1}{3}(-18x + 12)=nx-4 $ (assuming the original was $ \frac{1}{3}(-18x + 12)=nx - 4 $)
## Step1: Distribute $\frac{1}{3}$ on the left
$ \frac{1}{3}\times(-18x)+\frac{1}{3}\times12=-6x + 4 $
## Step2: Set equal to right side
$ -6x + 4=nx - 4 $
For the coefficients of $x$ to be equal (assuming $n$ is a constant), $n=-6$
Check the constant term: Left side constant is 4, right side constant is - 4. Wait, that's not equal. Maybe the equation is $ \frac{1}{3}(-18x + 12)=n - 4 $ (without the $x$ on the right)
## Step1: Distribute $\frac{1}{3}$
$ -6x + 4=n - 4 $
## Step2: Solve for $n$
$ n=-6x + 8 $
But if we assume the equation is $ \frac{1}{3}(-18x + 12)=n - 4 $ and we want $n$ as a constant, then there is a mistake. If the equation is $ \frac{1}{3}(-18x + 12)=nx - 4 $ and we made a mistake in the sign, maybe it's $ \frac{1}{3}(-18x + 12)=nx + 4 $
Then:
$ -6x + 4=nx + 4 $
Subtract 4: $ -6x=nx $
$n=-6$

### 10. $ 1.27-\frac{35}{100}=\frac{n}{100}+\frac{35}{100} $
## Step1: Simplify $1.27$ as a fraction. $1.27=\frac{127}{100}$
## Step2: Substitute into the equation
$ \frac{127}{100}-\frac{35}{100}=\frac{n}{100}+\frac{35}{100} $
## Step3: Combine fractions on the left
$ \frac{127 - 35}{100}=\frac{n + 35}{100} $
$ \frac{92}{100}=\frac{n + 35}{100} $
## Step4: Multiply both sides by 100
$ 92=n + 35 $
## Step5: Subtract 35 from both sides
$ n=92 - 35=57 $
# Answer: $ n = 57 $

Since the user may want the solutions for each equation, here are the answers for the ones we could solve as constants:

1. $ n = 3.3 $
2. $ n = 1.6 $
3. $ n = 6 $
6. $ n = 4 $
8. $ n = 8 $
10. $ n = 57 $

For the other equations, there may be typos or they are solved for $n$ in terms of $x$.

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QUESTION IMAGE

Question

Explanation:

1. \( 0.5(-4.2x + 6.6) = -2.1x + n \)

Step1: Distribute 0.5

Step2: Subtract \(-2.1x\) from both sides

Answer:

2. \( 0.2(12x + 8) = 2.4x + n \)

Step1: Distribute 0.2

Step2: Subtract \(2.4x\) from both sides