How many of the following equations have the solution set {5}%0D%0A{%0D%0A5%0D%0A}%0D%0A ?%0D%0A%0D%0A2(x−3)+1=5%0D%0A2%0D%0A(%0D%0A𝑥%0D%0A−%0D%0A3%0D%0A)%0D%0A+%0D%0A1%0D%0A=%0D%0A5%0D%0A %0D%0A%0D%0A3b15=1%0D%0A3%0D%0A𝑏%0D%0A15%0D%0A=%0D%0A1%0D%0A %0D%0A%0D%0A2h−30=40

Answer 1

To determine how many of the given equations have the solution set \({5}\), we will solve each equation for the variable and check if the solution is \(5\).

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

   \[ 2(x - 3) + 1 = 5 \] Subtracting \(1\) from both sides: \[ 2(x - 3) = 4 \] Dividing by \(2\): \[ x - 3 = 2 \] Adding \(3\) to both sides: \[ x = 5 \]

   Solution: \(5\)

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

   To solve for \(b\): \[ b^{15} = \frac{1}{3} \] Then: \[ b = \left(\frac{1}{3}\right)^{\frac{1}{15}} \]

   Solution: \(b \neq 5\)

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

   \[ 2h - 30 = 40 \] Adding \(30\) to both sides: \[ 2h = 70 \] Dividing both sides by \(2\): \[ h = 35 \]

   Solution: \(35 \neq 5\)

After checking each equation, we find that only the first equation yields the solution \(5\).

Thus, only 1 of the equations has the solution set \({5}\).