Which equation matches the solution set of {5}?(1 point)

Responses

3x5+4=7
Start Fraction 3 x over 5 End Fraction plus 4 equals 7

x+x−9=1+x
x plus x minus 9 equals 1 plus x

2x−20=30
2 x minus 20 equals 30

x2−10=15

1 answer

To find the equation that matches the solution set of {5}, we need to solve each equation and see which one has 5 as its solution.

  1. 3x/5 + 4 = 7 \[ 3x/5 + 4 = 7 \] Subtract 4 from both sides: \[ 3x/5 = 3 \] Multiply both sides by 5: \[ 3x = 15 \] Divide both sides by 3: \[ x = 5 \]

  2. x + x - 9 = 1 + x \[ 2x - 9 = 1 + x \] Subtract x from both sides: \[ x - 9 = 1 \] Add 9 to both sides: \[ x = 10 \]

  3. 2x - 20 = 30 \[ 2x - 20 = 30 \] Add 20 to both sides: \[ 2x = 50 \] Divide both sides by 2: \[ x = 25 \]

  4. x^2 - 10 = 15 \[ x^2 - 10 = 15 \] Add 10 to both sides: \[ x^2 = 25 \] Take the square root of both sides: \[ x = 5 \quad \text{or} \quad x = -5 \]

From the calculations, the first equation \(3x/5 + 4 = 7\) has the solution \(x = 5\), and the fourth equation \(x^2 - 10 = 15\) also has \(x = 5\) (along with \(x = -5\)).

Therefore, the equations that match the solution set of {5} are:

  • 3x/5 + 4 = 7
  • x^2 - 10 = 15

However, if we are looking for only one equation that matches specifically {5}, the best choice is:

  • 3x/5 + 4 = 7.