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Welcome to our lesson on first-degree equations with one unknown! These are fundamental algebraic equations where we need to find the value of a variable. Think of an equation like a balance scale - both sides must be equal. Today we'll learn how to solve these step by step.
To solve equations, we use inverse operations. Let's solve 2x plus 3 equals 11. First, we subtract 3 from both sides to eliminate the constant term. This gives us 2x equals 8. Next, we divide both sides by 2 to isolate x. Our solution is x equals 4. Remember, whatever we do to one side, we must do to the other side to keep the equation balanced.
It's crucial to check your solution. Let's verify that x equals 4 is correct. We substitute 4 for x in the original equation: 2 times 4 plus 3 equals 11. Calculating the left side: 8 plus 3 equals 11. Since both sides equal 11, our solution is verified! This checking step ensures we haven't made any calculation errors.
Let's look at more examples. First, negative 3x plus 7 equals 1. We subtract 7 from both sides to get negative 3x equals negative 6, then divide by negative 3 to get x equals 2. Second, x over 2 plus 5 equals 8. We subtract 5 to get x over 2 equals 3, then multiply by 2 to get x equals 6. Third, when variables appear on both sides like 5x minus 2 equals 3x plus 4, we collect like terms: 5x minus 3x equals 4 plus 2, giving us 2x equals 6, so x equals 3.
Let's summarize what we've learned about first-degree equations. The general form is ax plus b equals c, and the solution is x equals c minus b, all divided by a. Remember these key steps: identify the variable and constants, use inverse operations to isolate the variable, and always check your solution. The most important rule is to keep the equation balanced - whatever you do to one side, you must do to the other. With practice, solving these equations becomes second nature. Great job learning about first-degree equations!