Add (1)/(2) to both sides of the equation.

Here are the solutions to the equations: a) Solve 3z - (1)/(2) = (5)/(4) Step 1: Add (1)/(2) to both sides of the equation. 3z = (5)/(4) + (1)/(2) Step 2: Find a common denominator for the fractions on the right side and add them. 3z = (5)/(4) + (2)/(4) 3z = (7)/(4) Step 3: Divide both sides by 3. z = (7)/(4) × (1)/(3) z = (7)/(12) Step 4: Check the solution. 3((7)/(12)) - (1)/(2) = (7)/(4) - (1)/(2) = (7)/(4) - (2)/(4) = (5)/(4) The solution is correct. z = (7)/(12) b) Solve x - 18 = 36 Step 1: Add 18 to both sides of the equation. x = 36 + 18 x = 54 Step 2: Check the solution. 54 - 18 = 36 The solution is correct. x = 54 c) Solve 4x + 6 = 14 Step 1: Subtract 6 from both sides of the equation. 4x = 14 - 6 4x = 8 Step 2: Divide both sides by 4. x = (8)/(4) x = 2 Step 3: Check the solution. 4(2) + 6 = 8 + 6 = 14 The solution is correct. x = 2 d) Solve (108)/(27) = 3v - 29 Step 1: Simplify the left side of the equation. 4 = 3v - 29 Step 2: Add 29 to both sides of the equation. 4 + 29 = 3v 33 = 3v Step 3: Divide both sides by 3. v = (33)/(3) v = 11 Step 4: Check the solution. 3(11) - 29 = 33 - 29 = 4 The solution is correct. v = 11 e) Solve 2x - 9 = 16 Step 1: Add 9 to both sides of the equation. 2x = 16 + 9 2x = 25 Step 2: Divide both sides by 2. x = (25)/(2) Step 3: Check the solution. 2((25)/(2)) - 9 = 25 - 9 = 16 The solution is correct. x = (25)/(2) f) Solve (x)/(5) = 10 Step 1: Multiply both sides of the equation by 5. x = 10 × 5 x = 50 Step 2: Check the solution. (50)/(5) = 10 The solution is correct. x = 50 g) Solve (2)/(3)y = 1.6 Step 1: Convert the decimal to a fraction. 1.6 = (16)/(10) = (8)/(5) So the equation is: (2)/(3)y = (8)/(5) Step 2: Multiply both sides by the reciprocal of (2)/(3), which is (3)/(2). y = (8)/(5) × (3)/(2) Step 3: Simplify the multiplication. y = (24)/(10) y = (12)/(5) y = 2.4 Step 4: Check the solution. (2)/(3)((12)/(5)) = (24)/(15) = (8)/(5) = 1.6 The solution is correct. y = (12)/(5) or 2.4 h) Solve (1)/(4) - (3)/(4)x = (5)/(4) Step 1: Subtract (1)/(4) from both sides of the equation. -(3)/(4)x = (5)/(4) - (1)/(4) -(3)/(4)x = (4)/(4) -(3)/(4)x = 1 Step 2: Multiply both sides by -(4)/(3). x = 1 × (-(4)/(3)) x = -(4)/(3) Step 3: Check the solution. (1)/(4) - (3)/(4)(-(4)/(3)) = (1)/(4) - (-1) = (1)/(4) + 1 = (1)/(4) + (4)/(4) = (5)/(4) The solution is correct. x = -(4)/(3) i) Solve (x)/(4) = (1)/(16) Step 1: Multiply both sides of the equation by 4. x = (1)/(16) × 4 Step 2: Simplify the right side. x = (4)/(16) x = (1)/(4) Step 3: Check the solution. (1/4)/(4) = (1)/(4) × (1)/(4) = (1)/(16) The solution is correct. x = (1)/(4) j) Solve 2a - 99 = 29 Step 1: Add 99 to both sides of the equation. 2a = 29 + 99 2a = 128 Step 2: Divide both sides by 2. a = (128)/(2) a = 64 Step 3: Check the solution. 2(64) - 99 = 128 - 99 = 29 The solution is correct. a = 64 k) Solve (5)/(4)v - (2)/(3) = (1)/(3) Step 1: Add (2)/(3) to both sides of the equation. (5)/(4)v = (1)/(3) + (2)/(3) Step 2: Simplify the right side. (5)/(4)v = (3)/(3) (5)/(4)v = 1 Step 3: Multiply both sides by the reciprocal of (5)/(4), which is (4)/(5). v = 1 × (4)/(5) v = (4)/(5) Step 4: Check the solution. (5)/(4)((4)/(5)) - (2)/(3) = 1 - (2)/(3) = (3)/(3) - (2)/(3) = (1)/(3) The solution is correct. v = (4)/(5) l) Solve 2x - (1)/(3) = (7)/(4) Step 1: Add (1)/(3) to both sides of the equation. 2x = (7)/(4) + (1)/(3) Step 2: Find a common denominator for the fractions on the right side and add them. The common denominator for 4 and 3 is 12. 2x = (7 × 3)/(4 × 3) + (1 × 4)/(3 × 4) 2x = (21)/(12) + (4)/(12) 2x = (25)/(12) Step 3: Divide both sides by 2. x = (25)/(12) × (1)/(2) x = (25)/(24) Step 4: Check the solution. 2((25)/(24)) - (1)/(3) = (25)/(12) - (1)/(3) = (25)/(12) - (4)/(12) = (21)/(12) = (7)/(4) The solution is correct. x = (25)/(24) Drop the next question! 📸