Equivalent equation
- 1. Equivalent Equations Equivalent equations are equation which have the same solution sets if a certain operation is applied to the equations. Equivalent equations are symbolized by the symbol ”⇔” Equation 3x + 6 = 9 and x + 2 = 3 have the same solution. So, they are equivalent. Do equations 3x + 6 = 9 and x + 2 = 3 have the same solution?
- 2. Exercise Try to make some examples of “Equivalent Equations”!
- 3. Solving Equation of Fraction Form Solution: Method I : ⇔ ⇔ ⇔ ⇔ ⇔ ⇔ ⇔ ⇔ Both sides are multiplied by 5Both sides are multiplied by 5 Both sides are added by 4Both sides are added by 4 Both sides are divided by 6Both sides are divided by 6 Determine the solution of equation ( ) 623 5 2 =−x ( ) 623 5 2 =−x
- 4. Method II : ⇔ ⇔ ⇔ ⇔ ⇔ ⇔ 6 5 4 5 6 =−x 5 4 6 5 4 5 4 5 6 +=+−x 5 4 6 5 6 =x 5 34 6 5 5 6 6 5 ×=× x 6 34 =x 6 4 5=x Both sides are added byBoth sides are added by 5 4 Both sides are multiplied byBoth sides are multiplied by 6 5 ( ) 623 5 2 =−x
- 5. To determine the solution of fraction equation is by using some methods: 1. Change the equation into an equivalent equation but doesn’t consist of fraction anymore. By multiplying with its LCM 2. Without changing the equation into a kind of equivalent equation An equation in fraction form, is an equation that its variable consist of fraction or the Constanta is in fraction form, or both of them are in fraction form.
- 6. Application of Linear Equation with One Variable in Daily Life One variable equation is often used in the daily life. If you face a word problem, pay attention to the following several things. 1.Comprehend the problem so you acquire the known things and the question. 2.State the questions in variables, such as x. 3.Write the mathematical model / sentence according to the known situation. 4.Solve the mathematical sentence. 5.Recheck the solution.
- 7. The Following are Several Terms commonly Used in a Word Problem and How to Write it No Terms How to Write 1. The sum of m and n m + n 2. The difference between m and n m-n 3. Product of m and n m × n 4. Quotient m : n 5. The inverse of m 6. Inverse of the sum of m and n 7. Inverse of the difference between m and n, m > n 8. Square of sum of m and n (m+n)2 9. Sum of square of m and n m2 + n2 10. Square of difference m and n (m-n)2 11. Difference of square of m and n, m2 > n2 m2 - n2