Help on solving linear equations?

Question

1)

1/2(6x+3) - 8x - (3x-9) = 13/2
2)

5.2 (3x-7) - (x+9)=-38.1
3)

4z-19+(3z+2)=6z-12
4)

73-(b+8)-2(3b+4)=6b-2(b-5)+69
5)

0.5(x+2)-(3x+8)=1.6(x-2)+9

Answer 1

2) 5.2 (3x-7) - (x+9)=-38.1

[ Multiply the terms using FOIL ( first outer inner last)  method

The general form is  (a +b) (c+ d) = ac + ad + bc + bd ]

Simplify

(5.2)(3x) - (5.2)(7) - (x+9) = - 38.1

Simplify

15.6 x - 36.4 - x - 9 = - 38.1

.15.6 x - x - 36.4 - 9 = - 38.1

14.6 x - 45.4 = - 38.1

Add  45.4 to each side

14.6 x - 45.4 + 45.4= - 38.1 + 45.4

Simplify

14.6 x = 7.3

Divide each side by 14.6

(14.6 x)(14.6) = (7.3)(14.6)

Simplify

x = 0.5

3) 4z-19+(3z+2)=6z-12

4z-19+(3z+2)=6z-12

4z - 19 + 3z + 2 = 6z - 12

Simplify

7z - 17 = 6z - 12

Subtract 6z from each side.

7z - 17 -6z = 6z - 12 - 6z

Simplify

z - 17 = -12

Add 17 to each side

z - 17 + 17 = - 12 + 17

Simplify

z = 5

4) 73-(b+8)-2(3b+4)=6b-2(b-5)+69

73-(b+8)-2(3b+4)=6b-2(b-5)+69

[ Multiply the terms using FOIL ( first outer inner last)  method

The general form is  (a +b) (c+ d) = ac + ad + bc + bd ]

73 - b - 8 + (-2)(3b) + (-2)(4) = 6b + (-2)(b) + (-2)(-5) + 69

Simplify

73 - b - 8 -6b - 8 = 6b - 2b + 10 + 69

73 - 16 - 7b = 4b + 79

57 - 7b = 4b + 79

Add '7b' to each side

57 - 7b + 7b = 4b + 79 + 7b

Simplify

57 = 11b + 79

Subtract 79 from each side.

57 - 79 = 11b + 79 - 79

Simplify

- 22 = 11b

Divide each side by 11

-22 / 11 = 11b / 11

- 2 = b

5)  0.5(x+2)-(3x+8)=1.6(x-2)+9

0.5(x+2)-(3x+8)=1.6(x-2)+9

[ Multiply the terms using FOIL ( first outer inner last)  method

The general form is  (a +b) (c+ d) = ac + ad + bc + bd ].

(0.5)(x) + (0.5)(2) - (3x+8) = (1.6)(x) + (1.6)(-2) + 9

Simplify

0.5x + 1 - 3x - 8 = 1.6x - 3.2 + 9

Simplify

- 2.5x - 7 = 1.6x + 5.8

Add '2.5x' to each side

- 2.5x - 7 + 2.5 x = 1.6x + 5.8 + 2.5x

Simplify

- 7 = 4.1x + 5.8

Subtract '5.8' from each side.

- 7 - 5.8 = 4.1x + 5.8 - 5.8

Simplify

- 13.8 = 4.1x

Divide each side by  '4.1'

(- 13.8 ) / 4.1 = (4.1x) / 4.1

- 3.36585 = x

There fore

x = - 3.36585

Comments

Solution for 0.5(x+2)-(3x+8)=1.6(x-2)+9 is x = 3.12195.

Answer 2

1) 

Apply Distributive Property: a(b + c) = ab + bc.

Group like terms.

Take least common multiple for the terms 3/2 and -9.

Subtract 21/2 from each side.

Apply Additive Inverse Property: a - a = 0.

Apply Additive Identity Property: a + 0 = a.

Since denominators are equal,subtract the numerators.

Divide each side by -8.

Cancel common terms.

The solution is x  = 1/2.

Answer 3

5) The equation is 0.5(x + 2) - (3x + 8) = 1.6(x - 2) + 9.

Apply Distributive Property: a(b + c) = ab + bc.

  0.5(x ) + 0.5(2)   - 1(3x) + (-1)(8) = 1.6(x ) - 1.6(2) + 9

0.5x + 1 - 3x - 8= 1.6x  - 3.2 + 9

Take right hand side terms to left hand side.

0.5x + 1 - 3x - 8 - 1.6x  + 3.2 - 9 = 0

Group like terms.

0.5x - 3x - 1.6x + 1 - 8 + 3.2 - 9 = 0

Combine like terms.

-4.1x - 12.8 = 0

Add 12.8 to each side.

-4.1x - 12.8 +12.8 = 0 + 12.8

Apply Additive Inverse Property: -a + a = 0.

-4.1x + 0 = 0 + 12.8

Apply Additive Identity Property: a + 0 = a.

-4.1x  = 12.8

Divide each side by -4.1.

-4.1x /-4.1 = 12.8/-4.1

Cancel common terms.

x  = 12.8/-4.1

x  = -3.12195.