Solve the equation algebraicly for the exact vaule of x check your work : the equation is 6 - 2/4 (x + 5) = 4x

x = 7/9

Step-by-step explanation:

Solve for x:

(-x - 5)/2 + 6 = 4 x

Put each term in (-x - 5)/2 + 6 over the common denominator 2: (-x - 5)/2 + 6 = 12/2 + (-x - 5)/2:

12/2 + (-x - 5)/2 = 4 x

12/2 + (-x - 5)/2 = ((-x - 5) + 12)/2:

(-x - 5 + 12)/2 = 4 x

Grouping like terms, -x - 5 + 12 = (12 - 5) - x:

((12 - 5) - x)/2 = 4 x

12 - 5 = 7:

(7 - x)/2 = 4 x

Multiply both sides by 2:

(2 (7 - x))/2 = 2×4 x

(2 (7 - x))/2 = 2/2×(7 - x) = 7 - x:

7 - x = 2×4 x

2×4 = 8:

7 - x = 8 x

Subtract 8 x from both sides:

7 + (-x - 8 x) = 8 x - 8 x

-x - 8 x = -9 x:

-9 x + 7 = 8 x - 8 x

8 x - 8 x = 0:

7 - 9 x = 0

Subtract 7 from both sides:

(7 - 7) - 9 x = -7

7 - 7 = 0:

-9 x = -7

Divide both sides of -9 x = -7 by -9:

(-9 x)/(-9) = (-7)/(-9)

(-9)/(-9) = 1:

x = (-7)/(-9)

Multiply numerator and denominator of (-7)/(-9) by -1:

 x = 7/9

(1 1/4x - 5 1/6) - (5/8x + 1 1/3)

1 1/4x - 5 1/6 - 5/8x - 1 1/3

(1 1/4x - 5/8x) - (5 1/6 + 1 1/3)

(1 1/4 - 5/8)x - (5 1/6 + 1 1/3)

*note
1 1/4 = 5/4 = 10/8
5 1/6 = 31/6
1 1/3 = 4/3 = 8/6

*thus your equation can now be written using additive/subtractive components with common denominators

(10/8 - 5/8)x - (31/6 + 8/6)

(5/8)x - (39/6)

ANSWER:

5/8x - 39/6

5/8x - 6 3/6

5/8x - 6 1/2