Question

1. ( 3 + 5y + 8 - y ) 8. ( \frac{1}{3}x + \frac{1}{2}x - \frac{2}{3}y ) 9. ( -13 + 6.3x + 3.9x + 14.1 - 5.7y + 2y )

Explanation:

To solve the problem of simplifying the algebraic expression (assuming the left - most expression is \(3 + 5x+8 - y\)):

Step 1: Identify like terms

In the expression \(3 + 5x+8 - y\), the constant terms are \(3\) and \(8\), and the terms with variables are \(5x\) and \(-y\).

Step 2: Combine the constant terms

We add the constant terms together. Using the addition operation for real numbers, we have \(3 + 8=11\).

Step 3: Write the simplified expression

After combining the constant terms, the simplified form of the expression \(3 + 5x+8 - y\) is \(5x - y+11\) (or \(11 + 5x-y\)).

If we consider the right - most expression \(- 13+6.3x + 3.9x+14.1-5.7y + 2y\):

Step 1: Identify like terms

• For the \(x\) - terms: \(6.3x\) and \(3.9x\)
• For the \(y\) - terms: \(-5.7y\) and \(2y\)
• For the constant terms: \(-13\) and \(14.1\)

Step 2: Combine the \(x\) - terms

Using the rule of adding like terms (adding the coefficients of \(x\)), we have \(6.3x+3.9x=(6.3 + 3.9)x = 10.2x\)

Step 3: Combine the \(y\) - terms

Adding the coefficients of \(y\), we get \(-5.7y + 2y=(-5.7 + 2)y=-3.7y\)

Step 4: Combine the constant terms

Adding the constant terms, we have \(-13 + 14.1 = 1.1\)

Step 5: Write the simplified expression

The simplified form of the expression \(-13+6.3x + 3.9x+14.1-5.7y + 2y\) is \(10.2x-3.7y + 1.1\)

If we take the middle expression (assuming it is \(-\frac{1}{3}x-\frac{1}{2}x-\frac{2}{3}y\)):

Step 1: Combine the \(x\) - terms

First, find a common denominator for the coefficients of \(x\). The common denominator of \(3\) and \(2\) is \(6\).
\(-\frac{1}{3}x-\frac{1}{2}x=-\frac{2}{6}x-\frac{3}{6}x=-\frac{2 + 3}{6}x=-\frac{5}{6}x\)

Step 2: Write the simplified expression

The simplified form of the expression \(-\frac{1}{3}x-\frac{1}{2}x-\frac{2}{3}y\) is \(-\frac{5}{6}x-\frac{2}{3}y\)

Since the image is a bit unclear, if you can provide a more precise description of the expression you want to simplify, we can give a more accurate solution.

Answer:

To solve the problem of simplifying the algebraic expression (assuming the left - most expression is \(3 + 5x+8 - y\)):

Step 1: Identify like terms

In the expression \(3 + 5x+8 - y\), the constant terms are \(3\) and \(8\), and the terms with variables are \(5x\) and \(-y\).

Step 2: Combine the constant terms

We add the constant terms together. Using the addition operation for real numbers, we have \(3 + 8=11\).

Step 3: Write the simplified expression

After combining the constant terms, the simplified form of the expression \(3 + 5x+8 - y\) is \(5x - y+11\) (or \(11 + 5x-y\)).

If we consider the right - most expression \(- 13+6.3x + 3.9x+14.1-5.7y + 2y\):

Step 1: Identify like terms

• For the \(x\) - terms: \(6.3x\) and \(3.9x\)
• For the \(y\) - terms: \(-5.7y\) and \(2y\)
• For the constant terms: \(-13\) and \(14.1\)

Step 2: Combine the \(x\) - terms

Using the rule of adding like terms (adding the coefficients of \(x\)), we have \(6.3x+3.9x=(6.3 + 3.9)x = 10.2x\)

Step 3: Combine the \(y\) - terms

Adding the coefficients of \(y\), we get \(-5.7y + 2y=(-5.7 + 2)y=-3.7y\)

Step 4: Combine the constant terms

Adding the constant terms, we have \(-13 + 14.1 = 1.1\)

Step 5: Write the simplified expression

The simplified form of the expression \(-13+6.3x + 3.9x+14.1-5.7y + 2y\) is \(10.2x-3.7y + 1.1\)

If we take the middle expression (assuming it is \(-\frac{1}{3}x-\frac{1}{2}x-\frac{2}{3}y\)):

Step 1: Combine the \(x\) - terms

First, find a common denominator for the coefficients of \(x\). The common denominator of \(3\) and \(2\) is \(6\).
\(-\frac{1}{3}x-\frac{1}{2}x=-\frac{2}{6}x-\frac{3}{6}x=-\frac{2 + 3}{6}x=-\frac{5}{6}x\)

Step 2: Write the simplified expression

The simplified form of the expression \(-\frac{1}{3}x-\frac{1}{2}x-\frac{2}{3}y\) is \(-\frac{5}{6}x-\frac{2}{3}y\)

Since the image is a bit unclear, if you can provide a more precise description of the expression you want to simplify, we can give a more accurate solution.