Question - Algebraic Equation Solving: Finding the Unknown Number
Solution:
The problem given can be solved by setting up an algebraic equation.Let's let the unknown number be x.According to the problem, "three times the sum of 8 and twice an unknown number is equal to 4 times the sum of 3 times the unknown number and 8."This can be written as:3(8 + 2x) = 4(3x + 8)Now, let's solve this equation step by step:1. Distribute the 3 into (8 + 2x): 3 * 8 + 3 * 2x = 24 + 6x2. Distribute the 4 into (3x + 8): 4 * 3x + 4 * 8 = 12x + 32Now the equation looks like this:24 + 6x = 12x + 323. We'll start by getting the x terms on one side and constants on the other: Subtract 6x from both sides: 24 = 12x - 6x + 32 24 = 6x + 324. Now subtract 32 from both sides: 24 - 32 = 6x -8 = 6x5. Finally, divide both sides by 6 to isolate x: -8 / 6 = x x = -4/3 or -1.33 (to two decimal places)So, the solution for the unknown number x is -4/3 or -1.33 when rounded to two decimal places.
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