Let's go through Sehyr's work step by step to identify the error and find the correct solution to the equation \( w^2 - 7 = 11 \).
-
Starting with the equation: \[ w^2 - 7 = 11 \]
-
Applying the Addition Property of Equality: Sehyr correctly adds 7 to both sides: \[ w^2 - 7 + 7 = 11 + 7 \] This simplifies to: \[ w^2 = 18 \]
-
Identifying the error: Sehyr incorrectly wrote \( w^{2} = 182 \), which is a mistake. The correct equation after the addition step should be: \[ w^2 = 18 \]
-
Solving for \( w \): To find \( w \), take the square root of both sides: \[ w = \pm \sqrt{18} \]
-
Simplifying \(\sqrt{18}\): \[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \] Therefore, the solutions are: \[ w = 3\sqrt{2} \quad \text{and} \quad w = -3\sqrt{2} \]
Finally, the correct solutions to the equation \( w^2 - 7 = 11 \) are: \[ w = 3\sqrt{2}, \quad w = -3\sqrt{2} \]
1 answer