If C, equals, x, plus, 8C=x+8 and D, equals, 2, x, plus, 10, commaD=2x+10, find an expression that equals 2, C, plus, 3, D2C+3D in standard form.

Answer 1

To solve for \( 2C + 3D \) using the given expressions for \( C \) and \( D \), we begin by substituting the values of \( C \) and \( D \).

1. The expression for \( C \) is given as: \[ C = x + 8 \]

2. The expression for \( D \) is given as: \[ D = 2x + 10 \]

Now we will calculate \( 2C \) and \( 3D \):

Step 1: Calculate \( 2C \)

\[ 2C = 2(x + 8) = 2x + 16 \]

Step 2: Calculate \( 3D \)

\[ 3D = 3(2x + 10) = 6x + 30 \]

Step 3: Combine \( 2C \) and \( 3D \)

Now we can find \( 2C + 3D \): \[ 2C + 3D = (2x + 16) + (6x + 30) \]

Combine like terms: \[ 2C + 3D = 2x + 6x + 16 + 30 = 8x + 46 \]

Final Expression

Thus, the expression \( 2C + 3D \) in standard form is: \[ \boxed{8x + 46} \]