Hi.
To solve this, we need to convert all the words to mathematical terms and then write an equation.
"Twice the sum of a number and 8":
First, we don't know the number, so we're going to call it "x."
Next, "twice the sum of a number" can be represented as 2x, while "and eight" would be shows as + 8.
2x + 8
"negative 4 times the number plus 4"
Again, the number - which we don't know - is "x."
-4x + 4
The problem says to set these equal to each other. So:
2x + 8 = -4x + 4
Now we combine terms.
6x = -4
x = -4/6 = -2/3
So x = - 2/3.
We can check plug in the value of x to our equation to see if we got it right.
2x + 8 = -4x + 4
2 (-2/3) + 8 = -4 (-2/3) + 4
-4/3 + 8 = 8/3 + 4
-4/3 + 24/3 = 8/3 + 12/3
20/3 = 20/3
We got it right!
