Solving Equations With Variables on Both Sides Lesson
Solving Equations With Variables on Both Sides Lesson Objective: To use what we already know about to solve multiple step equations with variables on both sides.
Tools for the Tool Distribut ive Prope rty Box!! g n i b m Co s m r e t e lik Add ition Sub trac & Pro t per ion ties of E qua lity n o i t a c i l p Multi n o i s i v i D & f o s e i t r Prope y t i l a u q E
Steps to Solve Equations with Variables on Both Sides v v v Eliminate ( ) on both sides of equation using the distributive property. Combine any like terms on both sides. Collect variable on one side of the equation Collect constants on the other side of the equation Solve
Use Steps to Solve Equation: 2(x + 7) + 3 = 4 x - 1 2 x + 14 + 3 = 4 x – 1 2 x + 17 = 4 x - 1 -2 x 17 = 2 x - 1 +1 +1 18 = 2 x 2 2 9= x 1) Eliminate ( ) --distribute 2) Combine like terms 3) Collect variables on same side – use inverse operation 4) Collect constants on same side – use inverse operations
Check - replace “x” with solution 2(x + 7) + 3 = 4 x - 1 2(9 + 7) + 3 = 4(9) - 1 2(16) + 3 = 4(9) - 1 32 + 3 = 36 - 1 35 = 35 X=9 1) Replace X = 9 2) Follow order of operations on both sides of equation 3) Checks is the solution to the equation
Use Steps to Solve Equation: 3 x + 14 = 5 x + 8 -3 x 14 = 2 x + 8 -8 -8 6 = 2 x 2 2 x= 3 2) Combine like terms 3) Collect variables on same side – use inverse operation 4) Collect constants on same side – use inverse operations
Use Steps to Solve Equation: 4(1 – 2 x) = 4 – 6 x 4 – 8 x = 4 - 6 x + 6 x 4 - 2 x = 4 -4 -4 -2 x = 0 -2 -2 x= 0 Get rid of ( ) -- distribute Get variables on same side – use inverse operation (add 6 x) Solve 2 step equation
Use Steps to Solve Equation: 9 + 5 x = 5 x + 9 -5 x 9=9 x = any real number Get variables on same side of equation – use inverse operation (subtract 5 x) The variables zeroed out and remaining is a true statement where a number is equal to itself – this is called an identity The solution is all real numbers
Use Steps to Solve Equation: 6 x – 1 = 6 x – 8 -6 x Get variables on same side of equation – use inverse operation (subtract 6 x) -1 = - 8 The variables zeroed out and remaining is a false statement where a number is equal to a different number, so there will be no number that will work in the equation. x = no solutions The solution is no real numbers or empty set bkevil
Review Steps to Solve Equations with Variables on Both Sides v 1) Get rid of ( ) on both sides of equation. v 2) Combine like terms on both sides. v 3) Get variable on one side of the equation. v 4) Solve 2 step equation by undoing what has been done to the variable. v 5) Remember 2 special cases when the variable zeros out. bkevil
The end bkevil
- Slides: 11