simplify 4b + 3c - 2b + 7c

Question

4/6x + 10/15y

1/2x + 1 3/10y

1/4x + 13/10y

1 1/4x + 1y

Answer 1

Let's simplify each expression step by step:

1. For the expression \(4b + 3c - 2b + 7c\):

   • Combine like terms for \(b\): \(4b - 2b = 2b\)
   • Combine like terms for \(c\): \(3c + 7c = 10c\)
   • Thus, the expression simplifies to: \[ 2b + 10c \]

2. For the expression \(\frac{4}{6}x + \frac{10}{15}y\):

   • Simplify \(\frac{4}{6}\) and \(\frac{10}{15}\): \(\frac{4}{6} = \frac{2}{3}\) and \(\frac{10}{15} = \frac{2}{3}\)
   • So, the expression becomes: \[ \frac{2}{3}x + \frac{2}{3}y \]

3. For the expression \(\frac{1}{2}x + 1 \frac{3}{10}y\):

   • Convert the mixed number to an improper fraction: \(1 \frac{3}{10} = \frac{10}{10} + \frac{3}{10} = \frac{13}{10}\)
   • The expression is now: \[ \frac{1}{2}x + \frac{13}{10}y \]

4. For the expression \(\frac{1}{4}x + \frac{13}{10}y\), it is already simplified.

5. For the expression \(1 \frac{1}{4}x + 1y\):

   • Convert the mixed number to an improper fraction: \(1 \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}\)
   • So the expression can be written as: \[ \frac{5}{4}x + 1y \quad \text{or just} \quad \frac{5}{4}x + y \]

In summary, the simplified expressions are:

1. \(2b + 10c\)
2. \(\frac{2}{3}x + \frac{2}{3}y\)
3. \(\frac{1}{2}x + \frac{13}{10}y\)
4. \(\frac{1}{4}x + \frac{13}{10}y\) (already simplified)
5. \(\frac{5}{4}x + y\)