1. $$ 11 x+2 x=13 y $$ 3. $$ 21 x+6-x-5 $$ Simplify the expression. 5. $$ 2(3 x+x) $$ 7. $$ 2 x+4-3 x+2+3 x $$ Find the sum or difference. 9. $$ (s+12)+(3 s-8) $$ 11. $$ (2-k)+3(-4 k+2) $$ (13.) $$ (n-8)-(-2 n+2) $$

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UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Solution:
  $$2\left(3x+x\right)$$
- step1: Add the terms:
  $$2\times 4x$$
- step2: Multiply the numbers:
  $$8x$$
Calculate or simplify the expression $$ 21 x+6-x-5 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$21x+6-x-5$$
- step1: Subtract the terms:
  $$20x+1$$
Calculate or simplify the expression $$ 2 x+4-3 x+2+3 x $$.
Simplify the expression by following steps:
- step0: Solution:
  $$2x+4-3x+2+3x$$
- step1: Calculate:
  $$2x+6$$
Calculate or simplify the expression $$ (s+12)+(3 s-8) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(s+12\right)+\left(3s-8\right)$$
- step1: Remove the parentheses:
  $$s+12+3s-8$$
- step2: Add the terms:
  $$4s+4$$
Calculate or simplify the expression $$ (n-8)-(-2 n+2) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(n-8\right)-\left(-2n+2\right)$$
- step1: Remove the parentheses:
  $$n-8-\left(-2n+2\right)$$
- step2: Remove the parentheses:
  $$n-8+2n-2$$
- step3: Add the terms:
  $$3n-10$$
Solve the equation $$ 11 x+2 x=13 y $$.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$11x+2x=13y$$
- step1: Add the terms:
  $$13x=13y$$
- step2: Swap the sides:
  $$13y=13x$$
- step3: Divide both sides:
  $$\frac{13y}{13}=\frac{13x}{13}$$
- step4: Divide the numbers:
  $$y=x$$
Calculate or simplify the expression $$ (2-k)+3(-4 k+2) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(2-k\right)+3\left(-4k+2\right)$$
- step1: Remove the parentheses:
  $$2-k+3\left(-4k+2\right)$$
- step2: Expand the expression:
  $$2-k-12k+6$$
- step3: Add the numbers:
  $$8-13k$$
Here are the detailed solutions for each of the problems:

1. **Equation:** $$ 11x + 2x = 13y $$

- Combine like terms on the left side:
     $$
     13x = 13y
     $$
   - Divide both sides by 13:
     $$
     y = x
     $$

2. **Expression:** $$ 21x + 6 - x - 5 $$

- Combine like terms:
     $$
     (21x - x) + (6 - 5) = 20x + 1
     $$

3. **Expression:** $$ 2(3x + x) $$

- Combine inside the parentheses:
     $$
     2(4x) = 8x
     $$

4. **Expression:** $$ 2x + 4 - 3x + 2 + 3x $$

- Combine like terms:
     $$
     (2x - 3x + 3x) + (4 + 2) = 2x + 6
     $$

5. **Expression:** $$ (s + 12) + (3s - 8) $$

- Combine like terms:
     $$
     (s + 3s) + (12 - 8) = 4s + 4
     $$

6. **Expression:** $$ (2 - k) + 3(-4k + 2) $$

- Distribute the 3:
     $$
     2 - k - 12k + 6 = 8 - 13k
     $$

7. **Expression:** $$ (n - 8) - (-2n + 2) $$

- Distribute the negative sign:
     $$
     n - 8 + 2n - 2 = 3n - 10
     $$

### Summary of Results:
1. $$ y = x $$
2. $$ 20x + 1 $$
3. $$ 8x $$
4. $$ 2x + 6 $$
5. $$ 4s + 4 $$
6. $$ 8 - 13k $$
7. $$ 3n - 10 $$
1. $$ y = x $$ 2. $$ 20x + 1 $$ 3. $$ 8x $$ 4. $$ 2x + 6 $$ 5. $$ 4s + 4 $$ 6. $$ 8 - 13k $$ 7. $$ 3n - 10 $$

Simplify the expression.

Find the sum or difference.

(13.)

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Simplify the expression. Find the sum or difference. (13.)