algebra basics

In this video, we will be looking at how to solve algebraic equations quickly. Let's start with an example: Question: Solve the equation (3x + 5) / 7 = 2 To solve this equation, it's important to understand what is happening to the variable x. We can think of it in terms of operations: x is multiplied by 3 5 is added to x the sum is divided by 7 the result is 2 To find the value of x, we will reverse these operations: Start with 2 Instead of multiplying by 7, divide by 7 Instead of adding 5, subtract 5 Instead of multiplying by 3, divide by 3 By following these steps, we find that x is equal to 3. We can check this by substituting it back into the equation. Let's try another example: Question: Solve the equation 5x - 8 / 3 = 4 Using the same method, we can determine the order of operations: x is multiplied by 5 8 is subtracted from x the difference is divided by 3 the result is 4 To find x, we reverse these operations: Start with 4 Instead of dividing by 3, multiply by 3 Instead of subtracting 8, add 8 Instead of multiplying by 5, divide by 5 Following these steps, we find that x is equal to 4. Checking the equation confirms our answer. Let's try a more complex example: Question: Solve the equation (x^2 + 7)^0.5 + 5 = 9 Again, we determine the order of operations: x is squared 7 is added to x^2 the sum is square rooted 5 is added to the square root the result is 9 To find x, we reverse these operations: Start with 9 Instead of adding 5, subtract 5 Instead of square rooting, square the number Instead of adding 7, subtract 7 Instead of squaring, find the square root Following these steps, we find that x is equal to 3. Substituting this value back into the equation confirms our answer. Let's try one more example: Question: Solve the equation 5x * √(30 - 5x * 6) = 6 Again, we determine the order of operations: x is multiplied by 5 6 is multiplied by 5x and subtracted from 30 the difference is square rooted the square root is multiplied by 4 the result is divided by 2 the final result is 6 To find x, we reverse these operations: Start with 6 Instead of dividing by 2, multiply by 2 Instead of multiplying by 4, divide by 4 Instead of square rooting, square the number Instead of subtracting 6, add 6 Instead of multiplying by 5, divide by 5 Following these steps, we find that x is equal to 8. Substituting this value First, let's solve the equation step by step: Multiply by 2: x * 2 = 6 Divide by 4: (x * 2) / 4 = 3 Square: (x * 2 / 4)^2 = 9 Add 6: (x * 2 / 4)^2 + 6 = 15 Divide by 5: ((x * 2 / 4)^2 + 6) / 5 = 3 Therefore, x equals 3. Now, let's substitute x = 3 into the equation: 5 * (5 * 3 - 6)^(1/2) * 4 / 2 = 6 So our answer is correct. Now, with practice, you'll be able to solve these equations more efficiently by recognizing the steps automatically. Hope this was helpful. See you next time!