Final answer:
To solve the equations, distribute any terms inside parentheses and then simplify by combining like terms. Isolate the variable on one side of the equation by adding or subtracting terms. Finally, solve for the variable by dividing both sides of the equation.
Step-by-step explanation:
- In the equation 7(x+2)=2x+39, we can start by distributing the 7 to the terms inside the parentheses: 7x + 14 = 2x + 39. Then, we can subtract 2x from both sides to isolate the x term: 7x - 2x + 14 = 39. Combining like terms, we have 5x + 14 = 39. Finally, we can subtract 14 from both sides to solve for x: 5x = 39 - 14, which simplifies to 5x = 25. Dividing both sides by 5, we find that x = 5.
- For the equation -3(x+10)=-x-14+2x, we can start by distributing the -3 to the terms inside the parentheses: -3x - 30 = -x - 14 + 2x. Combining like terms, we have -3x - 30 = x - 14. Adding 3x to both sides, we get -30 = 4x - 14. Adding 14 to both sides, we have -16 = 4x. Dividing both sides by 4, we find that x = -4.
- In the equation 8(x+2)=x+9, we can start by distributing the 8 to the terms inside the parentheses: 8x + 16 = x + 9. Subtracting x from both sides, we get 8x - x + 16 = 9. Combining like terms, we have 7x + 16 = 9. Finally, subtracting 16 from both sides, we find that 7x = 9 - 16, which simplifies to 7x = -7. Dividing both sides by 7, we get x = -1.
- In the equation 3(x+2)=2x-54-x, we can start by distributing the 3 to the terms inside the parentheses: 3x + 6 = 2x - 54 - x. Combining like terms, we have 3x + 6 = x - 54. Subtracting x from both sides, we get 2x + 6 = -54. Finally, subtracting 6 from both sides, we find that 2x = -54 - 6, which simplifies to 2x = -60. Dividing both sides by 2, we get x = -30.