4. Solve the equation justifying each step with the correct reasoning.
2(x+8)=2x+8
To solve the equation 2(x + 8) = 2x + 8, we will simplify both sides of the equation step-by-step while justifying each step.
Step 1: Distribute the 2 to the terms inside the parentheses on the left side.
2(x + 8) = 2x + 8
2x + 16 = 2x + 8
Reasoning: We distribute the 2 to each term inside the parentheses, which gives us 2 times x and 2 times 8.
Step 2: Subtract 2x from both sides of the equation.
2x + 16 - 2x = 2x + 8 - 2x
16 = 8
Reasoning: By subtracting 2x from both sides, we eliminate the 2x term on the right side, leaving us with a constant value.
Step 3: Evaluate the equation
16 = 8
Reasoning: Since 16 does not equal 8, there is no solution to this equation.
Conclusion: The equation 2(x + 8) = 2x + 8 has no solution.
To solve the equation 2(x+8) = 2x + 8, we will follow these steps:
Step 1: Distribute the 2 to the terms inside the parentheses.
2(x+8) becomes 2*x + 2*8, which simplifies to 2x + 16.
Step 2: Now, our equation becomes 2x + 16 = 2x + 8.
Step 3: Next, we want to isolate the variable, x, on one side of the equation. Let's eliminate 2x from both sides of the equation.
Subtracting 2x from both sides, we have:
(2x - 2x) + 16 = (2x - 2x) + 8
Simplifying,
16 = 8.
Step 4: When we get an equation like 16 = 8, which is obviously false, this indicates that the equation has no solution. This happens because we canceled out the x variable during the step 3, and we are left with a contradiction.
Therefore, the equation 2(x+8) = 2x + 8 has no solution.
Step 1: Distribute the 2 on the left side of the equation:
2(x+8) = 2x + 16
Reason: When we have a number multiplied by a expression inside parentheses, we need to distribute that number to each term inside the parentheses.
Step 2: Simplify both sides of the equation:
2x + 16 = 2x + 8
Reason: Distributing 2 to (x+8) results in 2x+16 and the right side remains the same.
Step 3: Subtract 2x from both sides of the equation:
2x - 2x + 16 = 2x - 2x + 8
Reason: We subtract 2x from both sides in order to isolate the terms containing x on one side of the equation.
Step 4: Simplify:
16 = 8
Reason: Subtracting 2x from 2x on the left side and 2x from 2x on the right side results in 0x, which simplifies to 0. Therefore, the equation simplifies to 16 = 8.
Step 5: Conclusion:
The equation 2(x+8) = 2x + 8 has no solution because 16 does not equal 8.
Reason: Since the equation simplifies to a false statement (16 = 8), we conclude that there is no value of x that will satisfy this equation.