Algebra with fractions - Worked solutions
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This document provides examples of solving algebraic fractions. In Example 1, it shows how to solve 1/2 + x = 2 by bringing the x term to one side of the equation, resulting in x = 1/2. Example 2 solves x/2 = 6 by multiplying both sides by 2 to isolate x, getting x = 12. Example 3 presents two methods for solving x^3 + 2 = 8: method 1 subtracts 2 from both sides and divides both sides by 3, giving x = 18; method 2 treats it as a fraction by finding a common denominator, adding the fractions, and then solving for x, also getting x = 18. Both methods provide the same answer.
Algebra with fractions - Worked solutions
- 1. Algebraic Fractions Worked Solutions Example 1: Example 1b: 1 2 + x = 2 Same principle applies. Bring the x to be by itself. x = 2 - 1 2 As the 1 2 is a positive number, you minus it from both sides. x =1 1 2 Method 2 Gets the exact same answer... 1 2 - 2 = -x We had to minus the x and then minus the 2 from either side to get the numbers on one side and the letters (pronumerals) on the other. -1 1 2 = -x Now, we get rid of the negative, by dividing it by -1 -11 2 -1 =1 because negative x is the same as -1x x =1 1 2 Now the x is on it's own, we have the answer. So it doesn't matter which side you take to which side as you get the same answer. Method 1 1 2 + x = 2 x = 2 - 1 2 x =1 1 2 Method 2 Gets the exact same answer... 1 2 - 2 = -x -1 1 2 = -x -11 2 -1 =1 x =1 1 2 Just the Math
- 2. Algebraic Fractions Worked Solutions Example 2: Example 3 – Done 2 different ways (Both are correct): Use the same principles now with the harder questions. An explanation of the problem to the right. x 2 = 6 This is the same as saying x ¸2 = 6 x 2 ´2 = 6´2 Doing this will get the x on its own, x =12 which is what we need to do. The Maths without the words.. x 2 = 6 x 2 ´ 2 = 6´2 x =12 x 3 + 2 = 8 1. You need to get the x on its own. As these problems get harder we add another skill to the mix. 2. We leave the bit with the x in it to last. x 3 + 2 -2 = 8- 2 x 3 = 6 Now we do the x bit. x 3 ´3= 6´3 x =18 This is the answer as x is on its own. Method 2: x 3 + 2 = 8 You can treat this as a fraction and just add it once you have the same denominator. x 3 + 6 3 = 8 or x + 6 3 = 8 x + 6 = 8´3 x + 6 = 24 x = 24- 6 x =18 You notice that you get the same answer.