Final answer:
To find the value of x in the expression 2x ⋅ 3² + 2}{x + 3} = 5, we need to solve the equation. By simplifying, expanding, rearranging, and factoring the equation, we can solve for x and determine that x = 1.
Therefore, the value of x in the given expression is x = 1. So the answer is b) 2.
Step-by-step explanation:
To find the value of x in the expression 2x ⋅ 3² + 2}{x + 3} = 5, we need to solve the equation. Here are the steps:
Step 1: Simplify the equation 2x ⋅ 3² + 2}{x + 3} = 5
Step 2: Multiply the terms inside the brackets by the term outside the brackets. This gives us 6x² + 6x + 6}{x + 3} = 5
Step 3: Multiply both sides of the equation by (x + 3) to eliminate the denominator. This gives us 6x² + 6x + 6 = 5(x + 3)
Step 4: Expand and simplify the equation. This gives us 6x² + 6x + 6 = 5x + 15
Step 5: Rearrange the equation to bring all terms to one side. This gives us 6x² + 6x + 6 - 5x - 15 = 0
Step 6: Combine like terms. This gives us 6x² + x - 9 = 0
Step 7: Solve the quadratic equation using factoring, completing the square, or the quadratic formula. In this case, we can factor the equation to get (2x + 3)(3x - 3) = 0
Step 8: Set each factor equal to zero and solve for x. This gives us 2x + 3 = 0 or 3x - 3 = 0
Step 9: Solve for x. For 2x + 3 = 0, subtract 3 from both sides to get 2x = -3 and then divide by 2 to get x = -3/2. For 3x - 3 = 0, add 3 to both sides to get 3x = 3 and then divide by 3 to get x = 1
Therefore, the value of x in the given expression is x = 1. So the answer is b) 2.