Step 1: Expand the brackets. 3(x + 4) = 21 3x + 12 = 21 Step 2: Subtract 12 from both sides. 3x + 12 - 12 = 21 - 12 3x = 9 Step 3: Divide both sides by 3. x = 3 Check: 3(3 + 4) = 3(7) = 21 ✓ Therefore, x = 3.Step 1: Expand both brackets. 4(2x - 1) = 3(x + 6) 8x - 4 = 3x + 18 Step 2: Subtract 3x from both sides. 8x - 3x - 4 = 3x - 3x + 18 5x - 4 = 18 Step 3: Add 4 to both sides. 5x - 4 + 4 = 18 + 4 5x = 22 Step 4: Divide both sides by 5. x = 22/5 = 4.4 Check: LHS = 4(2×4.4 - 1) = 4(7.8) = 31.2 RHS = 3(4.4 + 6) = 3(10.4) = 31.2 ✓ Therefore, x = 4.4 or 22/5.Step 1: Form the equation. Let the number be x. Multiply by 4: 4x Add 7: 4x + 7 Result is 35: 4x + 7 = 35 Step 2: Solve the equation. 4x + 7 = 35 4x = 35 - 7 4x = 28 x = 28 ÷ 4 x = 7 Check: 7 × 4 + 7 = 28 + 7 = 35 ✓ The number I thought of is 7.Step 1: Since y = 2x, substitute 2x for y in the second equation. x + y = 12 x + 2x = 12 3x = 12 x = 4 Step 2: Find y by substituting x = 4 into y = 2x. y = 2(4) = 8 Step 3: Check in both equations. y = 2x: 8 = 2(4) = 8 ✓ x + y = 12: 4 + 8 = 12 ✓ Therefore, x = 4 and y = 8.Method: Elimination (adding the equations) Step 1: Add the two equations together. x + y = 10 + x - y = 4 ___________ 2x = 14 Step 2: Solve for x. x = 14 ÷ 2 = 7 Step 3: Substitute x = 7 into the first equation. 7 + y = 10 y = 10 - 7 = 3 Step 4: Check in both equations. x + y = 10: 7 + 3 = 10 ✓ x - y = 4: 7 - 3 = 4 ✓ Therefore, x = 7 and y = 3.Step 1: Form the equations. Let the two numbers be x and y (where x > y). Sum is 25: x + y = 25 ... (1) Difference is 7: x - y = 7 ... (2) Step 2: Add equations (1) and (2). x + y = 25 + x - y = 7 ___________ 2x = 32 x = 16 Step 3: Substitute x = 16 into equation (1). 16 + y = 25 y = 25 - 16 = 9 Step 4: Check. Sum: 16 + 9 = 25 ✓ Difference: 16 - 9 = 7 ✓ The two numbers are 16 and 9.Step 1: Multiply both sides by 2 to remove the fraction. (x + 3)/2 = 7 (x + 3)/2 × 2 = 7 × 2 x + 3 = 14 Step 2: Subtract 3 from both sides. x + 3 - 3 = 14 - 3 x = 11 Check: (11 + 3)/2 = 14/2 = 7 ✓ Therefore, x = 11.
