7/26/2019 Int Notes Handout 01.01 Solve Equations 2-Step

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Integrated Math Notes: Solve Two-Step Equations

Obj: Solve two-step equations.

Deinition

! nu"ber is a solutionto an equation i substituting that nu"ber or the

variable "a#es the equation true. Two equations are equivalentequationsi the$ have the sa"e solutions.

E%a"ple &

'hat are the solutions to ( &) (& ) *x x + =

a+ x, x, / b+ x, ) x, 0

1+ x, x, 0 d+ None o These

Solution

!nswer: 21+

To 1he1# thatx, is a solution: To 1he1# thatx, 0 is a solution:

( ) ( )(

- &) - (& )

3 -) (& )

(& (& )

+ =

+ =

+ =

( ) ( )(

0 &) 0 (& )

43 0) (& )

(& (& )

+ =

+ =

+ =

2The question now be1o"es how to ind su1h solutions on our own5ro" s1rat1h. 6ortunatel$5 we have so"e general rules5 or principles5 to

guide us.+

The 7rin1iples o Equation Solving

&. The goal o equation solving is to isolate the variable.

(. 8se opposite operations to solve equations.

. 'hatever we do to one side o an equation5 we do to both sides.

2Seesaw 7rin1iple+

E%a"ple (

Solve and 1he1#: (x9 && , 4.

Solution

7/26/2019 Int Notes Handout 01.01 Solve Equations 2-Step

2/2

Integrated Math Notes: Solve Two-Step Equations

2This is a 2-step equationbe1ause there are two nu"bers hanging

around; the variable5x5 i.e. on the sa"e side o the equals sign. Sin1e5

our goal is to isolate thex5 we will 1an1el out these nu"bers5 using

opposite operations.+

( &&x -4

&&

=

+ &&

(

+

4/

(

x =

(

x, ((./