Question

Use the Distributive Property to solve the equation6(x-6)+6=8x-12. ​ The solution of the equation is nothing. ​(Type the value of​ x.)

Answer 1

9514 1404 393

Answer:

-9

Explanation:

The distributive property is used to eliminate parentheses.

6(x -6) +6 = 8x -12

6x -36 +6 = 8x -12 . . . . . . . distribute 6 to x and -6

-30 = 2x -12 . . . . . . . . . . . . .subtract 6x, collect terms

-18 = 2x . . . . . . . . . . . . . . . . add 12

-9 = x . . . . . . . . . . . . . . . . . . divide by 2

The value of x is -9.

_____

Check

6(-9 -6) +6 = 8(-9) -12

6(-15) +6 = -72 -12

-90 +6 = -84 . . . . . . . true

Answer 2

The solution of the equation is x = -9

Explanation:

∵ The equation is 6(x - 6) + 6 = 8x - 12

→ Use the distributive property to simplift the left sid

∵ 6(x - 6) = 6(x) - 6(6) ⇒ Distributive property

∴ 6(x - 6) = 6x - 36

∴ 6x - 36 + 6 = 8x - 12

→ Add the like terms in the left side

∴ 6x + (-36 + 6) = 8x - 12

∴ 6x + (-30) = 8x - 12

∴ 6x - 30 = 8x - 12

→ Subtract 8x from both sides

∴ 6x - 8x - 30 = 8x - 8x - 12

∴ -2x - 30 = -12

→ Add 30 to both sides

∴ -2x - 30 + 30 = -12 + 30

∴ -2x = 18

→ Divide both sides by -2

∵
`(-2x)/(-2)=(18)/(-2)`

∴ x = -9

∴ The value of x is -9