Solving Equations Finding Your Balance

Balance Remember that the Equal Sign Means Balance The equations are the same on both sides. 2+4=6 6=6

How to solve an Equation To solve for a variable you have to remember TWO things. 1) Try to Isolate the Variable (Isolate means get the variable by itself.) 2) What ever you do on one side of the equation, you have to do the same to the other side.

Example (Write this down!) Begin to isolate the variable x by completing the INVERSE OPERATION of 3 4x + 3 – 3 = 19 – 3 4x = 16 Simplify Inverse Operation of multiply is Divide. Divide both sides by 4 Simplify Solved! X = 4

Now Check! Substitute 4 every place you see an X 4(4) + 3 = 19 Solve using PEMDAS 16 + 3 = 19 19 = 19 True! It must be correct!

Try one S + 7 = 21 S + 7 – 7 = 21 – 7 Isolate the Variable by doing the inverse operation to BOTH SIDES S = 14 Simplify. Solved! 14 + 7 = 21 Check 21 = 21 Correct!

Harder One 3m – 2 = 7 3m – 2 + 2 = 7 + 2 3m = 9 3m/3 = 9/3 m = 3 Add the inverse to Isolate the Variable. Simplify Divide by 3 (inverse of Multiply) Solve! Check on your own.

Even Harder 45 = 5x + 35 45 – 35 = 5x +35 – 35 10 = 5x 10/5= 5x/5 Check 45 = 5(2) + 35 45 = 10 + 35 45 = 45

Division Isolate the Variable by subtracting 2 from each side. Inverse of Division is Multiplication. Multiply each side by the Denominator. Simplify Solved!

Variables on BOTH SIDES! 5x - 6 = - 12 - x Eliminate the 6 by adding 6 to both sides Simplify Eliminate (-x) by adding x to both sides Divide both sides by 6 Solved! Now check. 5x – 6 + 6 = -12 +6 – x 5x = -6 – x 5x + x = -6 –x + x 6x = -6 6x/6 = -6/6 x = -1

Check 5x - 6 = - 12 - x 5(-1)- 6 = -12 – (-1) -5 – 6 = -12 + 1 Substitute Simplify It Checks! 5(-1)- 6 = -12 – (-1) -5 – 6 = -12 + 1 -11 = -11

Practice Problems 2.) 4x + 6 = - 22 1.) 7x + 4 = 88 4.) 7x + 5 = 75

Practice Combine Like Terms then Solve 1) 6x - 4 + 7x = 9 2) 3x + 1 + 7x = - 119 3) x - 3 + 6x = 11 4) - 8 = x - 3x - 2 X = 1 X = -12 X = 2 X = 3