This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the linear equations: 1. 2x+5=-1 Step 1: Subtract 5 from both sides of the equation. 2x+5-5 = -1-5 2x = -6 Step 2: Divide both sides by 2. (2x)/(2) = (-6)/(2) x = -3 The final answer is -3. 2. 5x-4=-9 Step 1: Add 4 to both sides of the equation. 5x-4+4 = -9+4 5x = -5 Step 2: Divide both sides by 5. (5x)/(5) = (-5)/(5) x = -1 The final answer is -1. 3. (2x+3)/(5)=5 Step 1: Multiply both sides of the equation by 5. 5 × (2x+3)/(5) = 5 × 5 2x+3 = 25 Step 2: Subtract 3 from both sides. 2x+3-3 = 25-3 2x = 22 Step 3: Divide both sides by 2. (2x)/(2) = (22)/(2) x = 11 The final answer is 11. 4. (5x-4)/(2)=3 Step 1: Multiply both sides of the equation by 2. 2 × (5x-4)/(2) = 3 × 2 5x-4 = 6 Step 2: Add 4 to both sides. 5x-4+4 = 6+4 5x = 10 Step 3: Divide both sides by 5. (5x)/(5) = (10)/(5) x = 2 The final answer is 2. 5. (x)/(4)-5=x-2 Step 1: Add 5 to both sides of the equation. (x)/(4)-5+5 = x-2+5 (x)/(4) = x+3 Step 2: Subtract x from both sides. (x)/(4)-x = x+3-x (x)/(4)-(4x)/(4) = 3 -(3x)/(4) = 3 Step 3: Multiply both sides by 4. 4 × (-(3x)/(4)) = 3 × 4 -3x = 12 Step 4: Divide both sides by -3. (-3x)/(-3) = (12)/(-3) x = -4 The final answer is -4. 6. -(4)/(9)x+6=1-x Step 1: Subtract 6 from both sides of the equation. -(4)/(9)x+6-6 = 1-x-6 -(4)/(9)x = -x-5 Step 2: Add x to both sides. -(4)/(9)x+x = -x-5+x -(4)/(9)x+(9)/(9)x = -5 (5)/(9)x = -5 Step 3: Multiply both sides by (9)/(5). (9)/(5) × (5)/(9)x = -5 × (9)/(5) x = -9 The final answer is -9. 7. 3(x+1)=2x-4 Step 1: Distribute the 3 on the left side of the equation. 3x+3 = 2x-4 Step 2: Subtract 2x from both sides. 3x+3-2x = 2x-4-2x x+3 = -4 Step 3: Subtract 3 from both sides. x+3-3 = -4-3 x = -7 The final answer is -7. 8. 4(x-3)=2-3x Step 1: Distribute the 4 on the left side of the equation. 4x-12 = 2-3x Step 2: Add 3x to both sides. 4x-12+3x = 2-3x+3x 7x-12 = 2 Step 3: Add 12 to both sides. 7x-12+12 = 2+12 7x = 14 Step 4: Divide both sides by 7. (7x)/(7) = (14)/(7) x = 2 The final answer is 2. Send me the next one 📸