Equations …. are mathematical sentences stating that two expressions are equivalent.

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Presentation transcript:

Equations …. are mathematical sentences stating that two expressions are equivalent

How do you solve an equation? 2x + 4 = 10 - x Start with an equation 2x + 4 =10 – x +x + x Step 1 Variables need to be on the left side. Add x to both sides Whatever you do to one side you must do to the other too 3x + 4 = 10 Step 2 Combine “like” terms 3x + 4 = 10 - 4 - 4 Step 3 Numbers need to be on right side. Subtract 4 from both sides. 3x = 6 Step 4 Combine “like” terms Divide by the coefficient to get the value of 1x 3x = 6 3 3 Step 5 x = 2 Step 6 There is your solution

How do you know if you were correct? Equations can be checked quickly and easily by YOU. In our example our solution was x=2 2x + 4 = 10 - x Substitute the value you found for x back into the equation to see if the two sides are equal to each other. If they are equal then you were right  If x = 2 2(2) + 4 = 10 – 2 4 + 4 = 8 8 = 8

Solving Equations That Look Like… Fractions !!! Example #1 3x = 6 4 2 Step 1 Cross multiply. 3x = 6 6x = 24 Step 2 Divide by coefficient 6x = 24 6 6 x = 4 Step 3 Check 3(4) = 6 4 2 3 = 3

Example #2 (x + 1) + (x – 1) = - 4 2 3 Step 1 Find a common denominator for (x + 1) + (x – 1) = - 4 2 and 3 2 3 3 (x + 1) + 2 (x – 1) = - 4 6 6 3x + 3 + 2x – 2 = - 4 6 6 Step 2 Simplify 5x + 1 = -4 6 5x + 1 = -24 5x + 1 - 1 = - 24 - 1 Step 3 Divide by coefficient 5x = - 25 5 5 x = - 5 Don’t forget to check to see if you are correct