How many of the following equations have the solution set {5} ? 2(x−3)+1=5 3b15=1 2h−30=40 (1 point) The number of equations that have the solution set {5} is

1 answer

To determine how many of the given equations have the solution set {5}, we need to solve each equation individually and check if it yields the solution \( x = 5 \).

  1. Equation 1: \( 2(x - 3) + 1 = 5 \)

    \[ 2(x - 3) + 1 = 5 \] \[ 2(x - 3) = 5 - 1 \] \[ 2(x - 3) = 4 \] \[ x - 3 = \frac{4}{2} \] \[ x - 3 = 2 \] \[ x = 2 + 3 \] \[ x = 5 \]

    This equation has the solution \( x = 5 \).

  2. Equation 2: \( 3b = 15 \)

    \[ 3b = 15 \] \[ b = \frac{15}{3} \] \[ b = 5 \]

    This equation has the solution \( b = 5 \).

  3. Equation 3: \( 2h - 30 = 40 \)

    \[ 2h - 30 = 40 \] \[ 2h = 40 + 30 \] \[ 2h = 70 \] \[ h = \frac{70}{2} \] \[ h = 35 \]

    This equation does not have the solution \( h = 5 \).

Now, let's summarize the findings:

  • Equation 1: Has \( x = 5 \)
  • Equation 2: Has \( b = 5 \)
  • Equation 3: Does not have \( h = 5 \)

Therefore, 2 out of the 3 equations have the solution set {5}.

The number of equations that have the solution set {5} is 2.