(1) \( 5 x+6=2 x+15 \) (2) \( 7 x-4=20+3 x \) (3) \( 2 x+15=43-5 x \) (4) \( 3+4 x=9 x+13 \) (5) \( 2 x-10=44+8 x \) (6) \( -7 x-2=24-9 x \) (7) \( 27-11 x=x-33 \) (B) \( 21 x+6=17 x-26 \) (9) \( 11 x=8 x-6 \) (10) \( -x-29=13+2 x \) (11) \( -18+5 x=-12 x-1 \) (12) \( -9 x-21=35-x \) (13) \( 7 x-2=-2 x-29 \) (14) \( 36+15 x=17 x \) (15) \( -15-4 x=6-3 x \) (16) \( 12 x-9=8 x-37 \) (17) \( -5 x+40=6 x-70 \) (18) \( -x-2=1-2 x \)

Sure, let's solve each of the given linear equations step by step. --- ### **(1) \( 5x + 6 = 2x + 15 \)** \[ \begin{align*} 5x + 6 &= 2x + 15 \\ 5x - 2x &= 15 - 6 \\ 3x &= 9 \\ x &= \frac{9}{3} \\ x &= 3 \end{align*} \] **Solution:** \( x = 3 \) --- ### **(2) \( 7x - 4 = 20 + 3x \)** \[ \begin{align*} 7x - 3x &= 20 + 4 \\ 4x &= 24 \\ x &= \frac{24}{4} \\ x &= 6 \end{align*} \] **Solution:** \( x = 6 \) --- ### **(3) \( 2x + 15 = 43 - 5x \)** \[ \begin{align*} 2x + 5x &= 43 - 15 \\ 7x &= 28 \\ x &= \frac{28}{7} \\ x &= 4 \end{align*} \] **Solution:** \( x = 4 \) --- ### **(4) \( 3 + 4x = 9x + 13 \)** \[ \begin{align*} 3 - 13 &= 9x - 4x \\ -10 &= 5x \\ x &= \frac{-10}{5} \\ x &= -2 \end{align*} \] **Solution:** \( x = -2 \) --- ### **(5) \( 2x - 10 = 44 + 8x \)** \[ \begin{align*} 2x - 8x &= 44 + 10 \\ -6x &= 54 \\ x &= \frac{54}{-6} \\ x &= -9 \end{align*} \] **Solution:** \( x = -9 \) --- ### **(6) \( -7x - 2 = 24 - 9x \)** \[ \begin{align*} -7x + 9x &= 24 + 2 \\ 2x &= 26 \\ x &= \frac{26}{2} \\ x &= 13 \end{align*} \] **Solution:** \( x = 13 \) --- ### **(7) \( 27 - 11x = x - 33 \)** \[ \begin{align*} 27 + 33 &= x + 11x \\ 60 &= 12x \\ x &= \frac{60}{12} \\ x &= 5 \end{align*} \] **Solution:** \( x = 5 \) --- ### **(B) \( 21x + 6 = 17x - 26 \)** \[ \begin{align*} 21x - 17x &= -26 - 6 \\ 4x &= -32 \\ x &= \frac{-32}{4} \\ x &= -8 \end{align*} \] **Solution:** \( x = -8 \) --- ### **(9) \( 11x = 8x - 6 \)** \[ \begin{align*} 11x - 8x &= -6 \\ 3x &= -6 \\ x &= \frac{-6}{3} \\ x &= -2 \end{align*} \] **Solution:** \( x = -2 \) --- ### **(10) \( -x - 29 = 13 + 2x \)** \[ \begin{align*} -x - 2x &= 13 + 29 \\ -3x &= 42 \\ x &= \frac{42}{-3} \\ x &= -14 \end{align*} \] **Solution:** \( x = -14 \) --- ### **(11) \( -18 + 5x = -12x - 1 \)** \[ \begin{align*} 5x + 12x &= -1 + 18 \\ 17x &= 17 \\ x &= \frac{17}{17} \\ x &= 1 \end{align*} \] **Solution:** \( x = 1 \) --- ### **(12) \( -9x - 21 = 35 - x \)** \[ \begin{align*} -9x + x &= 35 + 21 \\ -8x &= 56 \\ x &= \frac{56}{-8} \\ x &= -7 \end{align*} \] **Solution:** \( x = -7 \) --- ### **(13) \( 7x - 2 = -2x - 29 \)** \[ \begin{align*} 7x + 2x &= -29 + 2 \\ 9x &= -27 \\ x &= \frac{-27}{9} \\ x &= -3 \end{align*} \] **Solution:** \( x = -3 \) --- ### **(14) \( 36 + 15x = 17x \)** \[ \begin{align*} 36 &= 17x - 15x \\ 36 &= 2x \\ x &= \frac{36}{2} \\ x &= 18 \end{align*} \] **Solution:** \( x = 18 \) --- ### **(15) \( -15 - 4x = 6 - 3x \)** \[ \begin{align*} -4x + 3x &= 6 + 15 \\ -x &= 21 \\ x &= -21 \end{align*} \] **Solution:** \( x = -21 \) --- ### **(16) \( 12x - 9 = 8x - 37 \)** \[ \begin{align*} 12x - 8x &= -37 + 9 \\ 4x &= -28 \\ x &= \frac{-28}{4} \\ x &= -7 \end{align*} \] **Solution:** \( x = -7 \) --- ### **(17) \( -5x + 40 = 6x - 70 \)** \[ \begin{align*} -5x - 6x &= -70 - 40 \\ -11x &= -110 \\ x &= \frac{-110}{-11} \\ x &= 10 \end{align*} \] **Solution:** \( x = 10 \) --- ### **(18) \( -x - 2 = 1 - 2x \)** \[ \begin{align*} -x + 2x &= 1 + 2 \\ x &= 3 \end{align*} \] **Solution:** \( x = 3 \) --- ### **Summary of Solutions:** 1. \( x = 3 \) 2. \( x = 6 \) 3. \( x = 4 \) 4. \( x = -2 \) 5. \( x = -9 \) 6. \( x = 13 \) 7. \( x = 5 \) 8. \( x = -8 \) *(Originally labeled as (B))* 9. \( x = -2 \) 10. \( x = -14 \) 11. \( x = 1 \) 12. \( x = -7 \) 13. \( x = -3 \) 14. \( x = 18 \) 15. \( x = -21 \) 16. \( x = -7 \) 17. \( x = 10 \) 18. \( x = 3 \) --- Feel free to reach out if you have any further questions or need additional explanations!