solving one & two step equations with the variable on 1

Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook

1

October 07, 2017

Oct 74:13 PM

Homework Assignment

The following examples have to be copied for next class

Example 1

The examples must be copied and ready for me to check once you come to class.

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11


2

October 07, 2017

Aug 34:48 PM

Steps to solving a linear equation.

If possible simplify each side of the equation removing grouping symbols.

If possible, combine like terms(MUST to be on the same side of the equation).

If the variable that you want to solve for is on both sides of the equation cancel out one of the variables.

Add (or subtract) the same real number or variable expression on both sides of the equation.

Multiply (or divide) by the same nonzero number on both sides of the equation.

1.

2.

3.

4.

5.


3

October 07, 2017

Aug 34:58 PM

EXAMPLE 1

Solve :

SOLUTION

–2 + x = –7

–2 + x = –7

x = –5

–2 + x = –7 +2 +2


4

October 07, 2017

Aug 35:30 PM

Verify that the solution is correct.

–2 + x = –7

Substitute –5 in for x, simplify and check that both sides of the equation are equal.

–2 + (–5) = –7

–2 – 5 = –7 –7 = –7

x = –5 does satisfy the equation.


5

October 07, 2017

Aug 35:35 PM

EXAMPLE 2

Solve :

SOLUTION

32= –6 + x + 11

9 = x + 5

32= –6 + x + 11

9 = x + 5

9 = x + 5 – 5 – 5

4 = x


6

October 07, 2017

Aug 35:46 PM

Verify that the solution is correct.

Substitute 4 in for x, simplify and check that both sides of the equation are equal.

x = 4, does satisfy the equation.

9 = x + 5 9 = 4 + 5

9 = 9


7

October 07, 2017

Aug 410:15 AM

EXAMPLE 3

Solve :

SOLUTION

Simplify each side of the equation, if possible.

x4 = 3

2 – 7 2

x4 = 9

– 7 2

x4 = 9

– 14

x4 =

–5


8

October 07, 2017

Aug 49:22 AM

x4 4 = –5 4

x4 4 = –20

x = –20

x4 =

–5


9

October 07, 2017

Aug 410:20 AM

EXAMPLE 4

Solve :

SOLUTION

18 9 – 8 = –3x

2 – 8 = –3x–6 = –3x

–6 = –3x

–6 = –3x–3 –3–6 = –3x–3 –3

2 = x


10

October 07, 2017

Aug 410:36 AM

EXAMPLE 5

Solve :

SOLUTION

x = 623

x = 623


11

October 07, 2017

Aug 410:39 AM

Option 1Multiply both sides of the equation by the reciprocal of the fraction.

x = 623

x = 623

32

32

x = 66

312

x =23

32

32

16

x = 4


12

October 07, 2017

Aug 410:50 AM

Option 2Eliminate the fraction by multiplying both sides of the equation by denominator.

After the fraction is eliminated use the appropriate steps to solve the equation.

x = 623

3x =12

x = 2 6232

x = 12232


13

October 07, 2017

Aug 411:06 AM

33x

312=

33x

312=

x = 4


14

October 07, 2017

Aug 412:03 PM

EXAMPLE 6

Solve :

SOLUTION

Simplify each side of the equation, if possible.

9x + 8 – 7x – 13= –11

9x + 8 – 7x – 13= –11

2x – 5= –11

2x – 5 = –11


15

October 07, 2017

Aug 412:10 PM

2x – 5= –11+

5 +

52x = –6

2x = –62 2

2x = –62 2x = –3


16

October 07, 2017

Aug 41:43 PM

EXAMPLE 7

Solve :

SOLUTION

17 = 9x + 2(–7x + 8) – 4

17 = 9x + 2(–7x + 8) – 4

17 = 9x – 14x +16 – 4

17 = –5x +12

17 = –5x +12


17

October 07, 2017

Aug 43:58 PM

17 = –5x +12–12 –125 = –5x 5 –5x

–5–5 =

5 –5x –5–5 =

–1= x


18

October 07, 2017

Aug 44:05 PM

EXAMPLE 8

Solve :

SOLUTIONPlace a 1 in front of the parentheses then distribute –1 to each of the terms.

–9 – (3x – 4) + 2x = – 11

–9 – 1(3x – 4) + 2x = – 11

–9 – 1(3x – 4) + 2x = – 11

–9 – 3x + 4 + 2x = – 11

–5 – 1x = – 11


19

October 07, 2017

Aug 44:12 PM

–5 – 1x = – 11+ 5 + 5

–1x = – 6

–1x – 6–1 –1=

–1x – 6= –1 –1

x = 6


20

October 07, 2017

Aug 59:52 AM

EXAMPLE 9

Solve :

SOLUTION

Place a 1 in front of any variable that does not have a coefficient and in front of the parentheses then distribute –1 to each of the terms.

–7x – (–6x + 5) + x = – 5

–7x – 1(–6x + 5) + 1x = – 5

–7x – 1(–6x + 5) + 1x = – 5

–7x + 6x – 5 + 1x = – 5


21

October 07, 2017

Aug 59:56 AM

–5 + 0x = – 5–5 + 0 = – 5

–5 = – 5

This equation is a special case when solving linear equations where the variable cancels out and only numbers remain. Whenever this happens your answer will be one of two choices.

If the equation is TRUE, where both sides of the equation are equal the solution is.

ALL REAL NUMBERS

Option 1


22

October 07, 2017

Aug 510:06 AM

If the equation is FALSE, where both sides of the equation are NOT equal , the solution is.

NO SOLUTION

Option 2


23

October 07, 2017

Aug 510:26 AM

EXAMPLE 10

Solve :

SOLUTION

x + 4 – x = 632

37

Eliminate all fractions in the equation by multiplying the entire equation by the least common multiple of all the denominators.


24

October 07, 2017

Aug 510:29 AM

x + 4 – x = 632

37

– x + 4 = 635

Option 1

– x + 4 = 635

Add or subtract the fractions that are like terms solve the equation from that point using the appropriate steps.

– x + 4 = 635

– 4 – 4

– x = 235


25

October 07, 2017

Aug 510:45 AM

– x = 235

53– 5

3–

– x =35

53– 5

3– 12

x =15 – 56

15

x = – 56

Multiply by the reciprocal of the coefficient to isolate the x variable.


26

October 07, 2017

Aug 510:29 AM

Eliminate all fractions in the equation by multiplying the entire equation by the least common multiple of all the denominators.

Option 2

x + 4 – x = 632

37

Both denominators are the number 3 so the least common multiple is also 3.

Multiply the entire equation by 3.

x + 4 – x = 632

373( )

x + 4 – x = 632

373( )


27

October 07, 2017

Aug 510:29 AM

x + 4 – x = 632

373 3 3 3

2x +12 – 7x = 18

x + 4 – x = 632

373 3 3 3

–5x +12 = 18–12 –12–5x =

6


28

October 07, 2017

Aug 511:20 AM

–5x 6–5 –5 =

–5x 6–5 –5 =

x = –

65


29

October 07, 2017

Aug 511:20 AM

EXAMPLE 11

Solve :

SOLUTION

x – 1

+ x =37

25–

38–

Both denominators are the numbers 2 & 3 so the least common multiple is 6.

Multiply the entire equation by 6.

6( )x – 1

+ x =37

25–

38–

x – 1

+

x =

37

25– 3

8–6 6 6 6


30

October 07, 2017

Aug 511:41 AM

–15x – 6

+ 14x = –16

–1x – 6

= –16

x – 1

+

x =

37

25– 3

8–6 6 6 623 2

3 5x – 1

+ 7777

x =– 8–6 2 2

–1x – 6

= –16


31

October 07, 2017

Aug 511:45 AM

–1x – 6

= –16

+ 6

+ 6

–1x

= –10

–1x

–1= –10–1

–1x

–1 = –10–1

x

= 10

solving one & two step equations with the variable on 1

Documents