To determine which equation matches the solution set of \({5}\), we will solve each equation for \(x\) and see if \(x = 5\) is the solution.
a) \(x + x - 9 = 1 + x\)
Combine like terms: \[ 2x - 9 = 1 + x \] Subtract \(x\) from both sides: \[ 2x - x - 9 = 1 \] \[ x - 9 = 1 \] Add 9 to both sides: \[ x = 10 \]
b) \(\frac{3x}{5} + 4 = 7\)
Subtract 4 from both sides: \[ \frac{3x}{5} = 3 \] Multiply both sides by 5: \[ 3x = 15 \] Divide both sides by 3: \[ x = 5 \]
c) \(x^2 + 10 = 15\)
Subtract 10 from both sides: \[ x^2 = 5 \] Taking the square root of both sides gives: \[ x = \sqrt{5} \text{ or } x = -\sqrt{5} \] (Neither solution is 5.)
d) \(2x - 20 = 30\)
Add 20 to both sides: \[ 2x = 50 \] Divide both sides by 2: \[ x = 25 \]
From the solutions, we find that:
- a) \(x = 10\)
- b) \(x = 5\) (which matches)
- c) \(x = \sqrt{5}\) or \(x = -\sqrt{5}\)
- d) \(x = 25\)
Therefore, the equation that matches the solution set of \({5}\) is \(b) \frac{3x}{5} + 4 = 7\).
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