Question

If B, equals, w, plus, 1B=w+1 and A, equals, 2, w, plus, 1, commaA=2w+1, find an expression that equals 2, B, plus, 3, A2B+3A in standard form.






Solve the problem just like the example below
⬇️
If C, equals, 3, x, squared, plus, 4, x
C=3x
2
+4x and
B, equals, 2, x, squared, minus, 7, comma
B=2x
2
−7, find an expression that equals
2, C, plus, 2, B
2C+2B in standard form.
C, equals, 3, x, squared, plus, 4, x
C=
3x
2
+4x
B, equals, 2, x, squared, minus, 7
B=
2x
2
−7
2, C, plus, 2, B
2C+2B
2, left parenthesis, 3, x, squared, plus, 4, x, right parenthesis, plus, 2, left parenthesis, 2, x, squared, minus, 7, right parenthesis
2(3x
2
+4x)+2(2x
2
−7)
6, x, squared, plus, 8, x, plus, 4, x, squared, minus, 14
6x
2
+8x+4x
2
−14
10, x, squared, plus, 8, x, minus, 14
10x
2
+8x−14

Answer 1

Let's solve for \(2B + 3A\) using the definitions provided:

1. We have \(B = w + 1\).
2. We also have \(A = 2w + 1\).

Now we need to calculate \(2B + 3A\):

\[
2B + 3A = 2(w + 1) + 3(2w + 1)
\]

Now, let’s expand both terms:

\[
2(w + 1) = 2w + 2
\]
\[
3(2w + 1) = 6w + 3
\]

Now we can combine these results:

\[
2B + 3A = (2w + 2) + (6w + 3)
\]
\[
= 2w + 6w + 2 + 3
\]
\[
= 8w + 5
\]

Therefore, the expression \(2B + 3A\) in standard form is:

\[
\boxed{8w + 5}
\]