If B, equals, w, plus, 10B=w+10 and C, equals, minus, w, minus, 1, commaC=−w−1, find an expression that equals B, plus, 2, CB+2C in standard form.
We can start by combining like terms within the expressions for B and C.
From the first equation, "B equals w plus 10B equals w plus 10," we can isolate B by subtracting w from both sides:
10B - B = w + 10 - w
9B = 10
B = 10/9
From the second equation, "C equals minus w minus 1 equals -w - 1," we can isolate C by adding w to both sides:
C + w = -w - 1 + w
C + w = -1
C = -1 - w
Now we can substitute the expressions for B and C into the expression for B + 2C:
B + 2C = (10/9) + 2(-1 - w)
Simplifying,
B + 2C = 10/9 - 2 - 2w
In standard form, we can write this as:
B + 2C = -18w/9 - 18/9 + 20/9
Combining like terms again:
B + 2C = (-18w - 18 + 20)/9
Finally, simplifying further:
B + 2C = (-18w + 2)/9
Therefore, an expression that equals B + 2C in standard form would be (-18w + 2)/9.