Which equation matches the solution set of {5}

Question

x+x-9=1+x
2x-20=30
x^2-10+15
3x/5+4=7

Answer 1

To determine which of the equations has the solution set of \({5}\), we need to solve each equation and check if \(x = 5\) is a solution.

1. Equation: \(x + x - 9 = 1 + x\)

   Simplifying, \[ 2x - 9 = 1 + x \] Subtract \(x\) from both sides: \[ x - 9 = 1 \] Add \(9\) to both sides: \[ x = 10 \]

2. Equation: \(2x - 20 = 30\)

   Adding \(20\) to both sides: \[ 2x = 50 \] Dividing by \(2\): \[ x = 25 \]

3. Equation: \(x^2 - 10 + 15 = 0\)

   This can be simplified to: \[ x^2 + 5 = 0 \] This does not have real solutions, since \(x^2 = -5\) leads to imaginary solutions.

4. Equation: \(\frac{3x}{5} + 4 = 7\)

   Subtract \(4\) from both sides: \[ \frac{3x}{5} = 3 \] Multiplying both sides by \(5\): \[ 3x = 15 \] Dividing by \(3\): \[ x = 5 \]

The only equation that has the solution \(x = 5\) is the last one, \(\frac{3x}{5} + 4 = 7\).

Thus, the answer is:

\(\frac{3x}{5} + 4 = 7\)