Question

1. which value of x is a solution of the equation 2x = x + 5?

a

one way
2x = x + 5
2(5) = 5 + 5
10 = 10 true
another way
2x = x + 5
−x −x
x = 5

does the equation have any other solutions?
no, the equation has exactly one solution.
yes, there are solutions other than x = 5.

Explanation:

To determine if the equation \(2x = x + 5\) has other solutions, we analyze the number of solutions for a linear equation in one variable. A linear equation of the form \(ax + b = cx + d\) (where \(a\), \(b\), \(c\), \(d\) are constants) has:

• Exactly one solution if \(a

eq c\) (the coefficients of \(x\) are different),

• No solutions if \(a = c\) and \(b

eq d\),

• Infinitely many solutions if \(a = c\) and \(b = d\).

For the equation \(2x = x + 5\), we can rewrite it as \(2x - x = 5\), which simplifies to \(x = 5\). Here, the coefficient of \(x\) on the left is \(2\) and on the right (after moving \(x\) to the left) is \(1\) (since \(2x - x=(2 - 1)x = x\)). Since the coefficient of \(x\) (the slope, in a sense) is non - zero ( \(2
eq1\) when we consider the standard form), this is a linear equation with a unique solution. So the equation has exactly one solution, and there are no other solutions.

Answer:

No, the equation has exactly one solution.