Given the equation 4x + 7 = 3(2x − 5), solve for the variable. Explain each step and justify your process.
Sam solved a similar equation below. Is Sam's solution correct? Explain why or why not.
5x − 1 = 2(x + 4)
5x − 1 = 2x + 8
7x − 1 = 8
7x = 7
x = 1
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Hint for the second part:- there is an error in the third line
- and in 4th line also
Sam's solution is unfortunately incorrect.
His/her faults lie in Steps 3-4. In Step 3, Sam reduces 5x - 1 = 2x + 8 to 7x - 1 = 8. This is incorrect, because Sam subtracts 2x from the right side of the equation but adds it to the left side of the equation.
A similar error is reflected in Step 4, where Sam adds 1 to the left side of the equation but subtracts 1 from the right side of the equation.
Redo Steps 3 and 4, this time making sure to sustain whatever operations Sam performs on one side of the equation to the other side of the equation. If you need to subtract anything from one side of the equation, make sure you subtract the same amount from the other side. Same with addition.