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 algebra problems: a) Solve for x: x+7=15 Step 1: Subtract 7 from both sides of the equation. x = 15 - 7 Step 2: Simplify the right side. x = 8 The solution is x=8. b) Solve for x: -3x=-6 Step 1: Divide both sides of the equation by -3. x = (-6)/(-3) Step 2: Simplify the fraction. x = 2 The solution is x=2. c) Solve for x: 9x-7=11 Step 1: Add 7 to both sides of the equation. 9x = 11 + 7 9x = 18 Step 2: Divide both sides by 9. x = (18)/(9) Step 3: Simplify the fraction. x = 2 The solution is x=2. d) Solve for x: (x)/(4)=-5 Step 1: Multiply both sides of the equation by 4. x = -5 × 4 Step 2: Perform the multiplication. x = -20 The solution is x=-20. e) Solve for x: -(x)/(3)+1=3 Step 1: Subtract 1 from both sides of the equation. -(x)/(3) = 3 - 1 -(x)/(3) = 2 Step 2: Multiply both sides by -3. x = 2 × (-3) Step 3: Perform the multiplication. x = -6 The solution is x=-6. f) Solve for x: (3x-1)/(2)=2 Step 1: Multiply both sides of the equation by 2. 3x-1 = 2 × 2 3x-1 = 4 Step 2: Add 1 to both sides. 3x = 4 + 1 3x = 5 Step 3: Divide both sides by 3. x = (5)/(3) The solution is x=(5)/(3). g) Solve for x: x-8=19 Step 1: Add 8 to both sides of the equation. x = 19 + 8 Step 2: Perform the addition. x = 27 The solution is x=27. h) Solve for x: 3x+5=29 Step 1: Subtract 5 from both sides of the equation. 3x = 29 - 5 3x = 24 Step 2: Divide both sides by 3. x = (24)/(3) Step 3: Simplify the fraction. x = 8 The solution is x=8. i) Solve for m: (m)/(3)=6 Step 1: Multiply both sides of the equation by 3. m = 6 × 3 Step 2: Perform the multiplication. m = 18 The solution is m=18. j) Solve for x: (1)/(2)(3x+1)+(1)/(3)(2x+10)=0 Step 1: Multiply the entire equation by the least common multiple of the denominators (2 and 3), which is 6, to eliminate the fractions. 6 · (1)/(2)(3x+1) + 6 · (1)/(3)(2x+10) = 6 · 0 3(3x+1) + 2(2x+10) = 0 Step 2: Distribute the numbers into the parentheses. 9x + 3 + 4x + 20 = 0 Step 3: Combine like terms (x terms and constant terms). (9x + 4x) + (3 + 20) = 0 13x + 23 = 0 Step 4: Subtract 23 from both sides of the equation. 13x = -23 Step 5: Divide both sides by 13. x = -(23)/(13) The solution is x=-(23)/(13). That's 2 down. 3 left today — send the next one.