Can you please solve all 15 questions from the picture I sent step-by-step?

Ghalti ke liye maafi chahta hoon! Bilkul, main aapki bheji hui picture ke **saare ke saare 15 questions** ko ek ek karke step-by-step yahan solve kar deta hoon taake aapko kahin aur na dekhna pare. --- ### **Questions (1 to 8): Solve the Linear Equations** #### **1. $3x - 12 + 4x = 6x + 6$** * **Step 1:** Left side par like terms ($3x$ aur $4x$) ko jama karein: $7x - 12 = 6x + 6$ * **Step 2:** $6x$ ko left side aur $-12$ ko right side par shift karein: $7x - 6x = 6 + 12$ * **Answer:** $\mathbf{x = 18}$ --- #### **2. $3(2y - 4) + 3y = 5(y - 4)$** * **Step 1:** Brackets ko multiply karke open karein: $6y - 12 + 3y = 5y - 20$ * **Step 2:** Left side par like terms ($6y$ aur $3y$) ko add karein: $9y - 12 = 5y - 20$ * **Step 3:** $5y$ ko left par aur $-12$ ko right par le jayein: $9y - 5y = -20 + 12$ $4y = -8$ * **Answer:** $y = \frac{-8}{4} \implies \mathbf{y = -2}$ --- #### **3. $3x - 2(2x - 5) = 2(x + 3) - 8$** * **Step 1:** Brackets open karein (negative sign ka khayal rakhein): $3x - 4x + 10 = 2x + 6 - 8$ * **Step 2:** Dono sides ko simplify karein: $-x + 10 = 2x - 2$ * **Step 3:** $x$ wali terms ek taraf aur numbers doosri taraf karein: $10 + 2 = 2x + x$ $12 = 3x$ * **Answer:** $x = \frac{12}{3} \implies \mathbf{x = 4}$ --- #### **4. $3x + \frac{1}{5} = 2 - x$** * **Step 1:** $x$ ko left side par shift karein aur $\frac{1}{5}$ ko right side par: $3x + x = 2 - \frac{1}{5}$ $4x = \frac{10}{5} - \frac{1}{5}$ $4x = \frac{9}{5}$ * **Answer:** $x = \frac{9}{5 \times 4} \implies \mathbf{x = \frac{9}{20}} \quad (\text{ya } \mathbf{0.45})$ --- #### **5. $\frac{x}{4} + \frac{x}{6} = \frac{x}{2} + \frac{3}{4}$** * **Step 1:** Denominators (4, 6, 2) ka LCM $12$ hai. Puri equation ko $12$ se multiply karein: $12\left(\frac{x}{4}\right) + 12\left(\frac{x}{6}\right) = 12\left(\frac{x}{2}\right) + 12\left(\frac{3}{4}\right)$ $3x + 2x = 6x + 9$ * **Step 2:** Simplify karein: $5x = 6x + 9$ $5x - 6x = 9$ $-x = 9$ * **Answer:** $\mathbf{x = -9}$ --- #### **6. $\frac{y + 4}{2y - 3} = \frac{2}{5}$** * **Step 1:** Cross-multiplication karein: $5(y + 4) = 2(2y - 3)$ $5y + 20 = 4y - 6$ * **Step 2:** Terms ko rearrange karein: $5y - 4y = -6 - 20$ * **Answer:** $\mathbf{y = -26}$ --- #### **7. $x - \left(2x - \frac{3x - 4}{7}\right) = \frac{4x - 27}{3} - 3$** * **Step 1:** Left Hand Side (LHS) ko simplify karein: $x - 2x + \frac{3x - 4}{7} = -x + \frac{3x - 4}{7} = \frac{-7x + 3x - 4}{7} = \frac{-4x - 4}{7}$ * **Step 2:** Right Hand Side (RHS) ko simplify karein: $\frac{4x - 27 - 9}{3} = \frac{4x - 36}{3}$ * **Step 3:** Dono sides ko barabar rakh kar cross-multiply karein: $\frac{-4x - 4}{7} = \frac{4x - 36}{3}$ $3(-4x - 4) = 7(4x - 36)$ $-12x - 12 = 28x - 252$ * **Step 4:** Solve for $x$: $-12 + 252 = 28x + 12x$ $240 = 40x$ * **Answer:** $x = \frac{240}{40} \implies \mathbf{x = 6}$ --- #### **8. $0.3x + 0.4 = 0.28x + 1.16$** * **Step 1:** $0.28x$ ko left side par aur $0.4$ ko right side par le jayein: $0.30x - 0.28x = 1.16 - 0.40$ $0.02x = 0.76$ * **Answer:** $x = \frac{0.76}{0.02} \implies \mathbf{x = 38}$ --- ### **Question 9: Select the ordered pairs which are solution points** *(Hum pairs $(x, y)$ ko equations mein put karke check karenge ke LHS = RHS aata hai ya nahi)* * **(a) $3x - y = -8$** * $(-1, 10) \rightarrow 3(-1) - 10 = -13 \neq -8$ (No) * $(3, 10) \rightarrow 3(3) - 10 = -1 \neq -8$ (No) * **$(-2, 2)$** $\rightarrow 3(-2) - 2 = -8$ **(Yes)** * **$(-1, 5)$** $\rightarrow 3(-1) - 5 = -8$ **(Yes)** * **Answer:** **$(-2, 2)$** aur **$(-1, 5)$** * **(b) $2x - y = -1$** * **$(0, 1)$** $\rightarrow 2(0) - 1 = -1$ **(Yes)** * **$(2, 5)$** $\rightarrow 2(2) - 5 = -1$ **(Yes)** * $(0, 0) \rightarrow 2(0) - 0 = 0 \neq -1$ (No) * **$(-2, -3)$** $\rightarrow 2(-2) - (-3) = -1$ **(Yes)** * **Answer:** **$(0, 1)$**, **$(2, 5)$**, aur **$(-2, -3)$** * **(c) $2x + y = 4$** * $(2, 3) \rightarrow 2(2) + 3 = 7 \neq 4$ (No) * $(1, 0.5) \rightarrow 2(1) + 0.5 = 2.5 \neq 4$ (No) * **$(0, 4)$** $\rightarrow 2(0) + 4 = 4$ **(Yes)** * $(-2, 2) \rightarrow 2(-2) + 2 = -2 \neq 4$ (No) * **Answer:** **$(0, 4)$** --- ### **Question 10: Find any three ordered pairs** * **(a) $y - x = 3 \implies y = x + 3$** * If $x = 0 \rightarrow y = 3 \implies \mathbf{(0, 3)}$ * If $x = 1 \rightarrow y = 4 \implies \mathbf{(1, 4)}$ * If $x = 2 \rightarrow y = 5 \implies \mathbf{(2, 5)}$ * **(b) $3x + 2y = -6 \implies 2y = -6 - 3x$** * If $x = 0 \rightarrow 2y = -6 \implies y = -3 \implies \mathbf{(0, -3)}$ * If $x = -2 \rightarrow 2y = -6 - 3(-2) = 0 \implies y = 0 \implies \mathbf{(-2, 0)}$ * If $x = 2 \rightarrow 2y = -6 - 3(2) = -12 \implies y = -6 \implies \mathbf{(2, -6)}$ --- ### **Word Problems (11 to 15)** #### **11. The sum of four consecutive odd numbers is 56. Find the greatest.** * **Step 1:** Let the four consecutive odd