Final answer:
The question involves solving four different linear equations and then checking if the solutions are reasonable. For each equation, we combine like terms, move variables to one side, and then isolate the variable to find the solution. The solutions should be substituted back into the original equations to check for their validity.
Step-by-step explanation:
The subject question involves solving linear equations and checking solutions for accuracy. Let's solve each equation step by step and check our solutions:
Solution A)
3x - 1 = 4x + 8 - x
Step 1: Combine like terms on both sides.
3x - 1 = 3x + 8
Step 2: Subtract 3x from both sides to get the variables on one side.
-1 = 8
This equation has no solution since -1 can never equal 8.
Solution B)
-10 + 5x = 7x - 4
Step 1: Subtract 5x from both sides.
-10 = 2x - 4
Step 2: Add 4 to both sides to isolate the variable term.
-6 = 2x
Step 3: Divide both sides by 2.
x = -3
This is the solution for equation B).
Solution C)
28 - 6x + x = 30 - 3x
Step 1: Combine like terms on both sides.
28 - 5x = 30 - 3x
Step 2: Add 5x to both sides.
28 = 30 + 2x
Step 3: Subtract 30 from both sides.
-2 = 2x
Step 4: Divide both sides by 2.
x = -1
This is the solution for equation C).
Solution D)
4x - 1 = 9x - 1 - 5x
Step 1: Combine like terms on the right side.
4x - 1 = 4x - 1
Since both sides of the equation are the same, this suggests that every x value is a solution. This is called an identity.
The next step after finding each solution is to substitute it back into the original equation to check if the solution is reasonable. This ensures the solution satisfies the original equation.