Question

Solve the equation -8(6x-12)+4= -10(x+8)+408 algebraically. answer as a reduced fraction.

Answer 1

The equation is -8(6x - 12) + 4 = -10 (x + 8) + 408

Let us simplify each side at first

-8(6x - 12) + 4

We will multiply the bracket by -8

(-8)(6x) + (-8)(-12) + 4 = -48 x + 96 + 4

Add the like terms 96 + 4

The left side is -48 x + 100

-10(x + 8) + 408 = (-10)(x) + (-10)(8) + 408 = -10x - 80 + 408

Add the like terms -80 + 408

The right side is -10x + 328

So the equation after simplifying is

-48 x + 100 = -10 x + 328

Add 10x to both sides

-48 x + 10 x + 100 = -10 x + 10 x + 328

-38 x + 100 = 328

Subtract 100 from both sides

-38 x + 100 - 100 = 328 - 100

-38 x = 228

Divide both sides by -38 to get x

`\begin{gathered} (-38x)/(-38)=(228)/(-38) \\ x=-6 \end{gathered}`

The solution of the equation is - 6

You can check the answer by substituting the value of x in each side the two sides must be equal