How many of the following equations have the solution set {5}

?

2(x−3)+1=5

3b/15=1

2h−30=40

(1 point)
The number of equations that have the solution set {5}
is
.
Remaining Attempts : 3

1 answer

To determine how many of the given equations have the solution set \({5}\), we will solve each equation and see if \(x = 5\) is the only solution.

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

    \(2(x - 3) + 1 = 5\)

    Subtract 1 from both sides:

    \(2(x - 3) = 4\)

    Divide by 2:

    \(x - 3 = 2\)

    Add 3 to both sides:

    \(x = 5\)

    So, the solution set for this equation is \({5}\).

  2. Equation: \(\frac{3b}{15} = 1\)

    Multiply both sides by 15:

    \(3b = 15\)

    Divide by 3:

    \(b = 5\)

    Therefore, the solution set for this equation is also \({5}\).

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

    Add 30 to both sides:

    \(2h = 70\)

    Divide by 2:

    \(h = 35\)

    Therefore, the solution set for this equation is \({35}\).

Now we summarize:

  • The first equation gives a solution set of \({5}\).
  • The second equation gives a solution set of \({5}\).
  • The third equation gives a solution set of \({35}\).

Thus, the total number of equations that have the solution set \({5}\) is 2.

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