7​(3xplus9​)equals11minus​(xplus3​) 

Let's solve the equation step by step:

The equation is:

\[
7(3x + 9) = 11 - (x + 3)
\]

### Step 1: Distribute on both sides.
Distribute the \(7\) on the left-hand side and the negative sign on the right-hand side.

\[
7 \cdot 3x + 7 \cdot 9 = 11 - x - 3
\]

This simplifies to:

\[
21x + 63 = 11 - x - 3
\]

### Step 2: Simplify both sides.
On the right-hand side, combine like terms:

\[
21x + 63 = 8 - x
\]

### Step 3: Move all terms involving \(x\) to one side.
Add \(x\) to both sides:

\[
21x + x + 63 = 8
\]

This simplifies to:

\[
22x + 63 = 8
\]

### Step 4: Move constant terms to the other side.
Subtract 63 from both sides:

\[
22x = 8 - 63
\]

This simplifies to:

\[
22x = -55
\]

### Step 5: Solve for \(x\).
Divide both sides by 22:

\[
x = \frac{-55}{22}
\]

Simplifying the fraction:

\[
x = -\frac{55}{22} = -\frac{5}{2}
\]

Thus, the solution is:

\[
x = -\frac{5}{2}
\]

### Do you have any questions or need further explanation?

Here are 5 related questions to practice:

1. Solve \( 5(2x + 7) = 3x - 9 \).
2. Simplify and solve \( 4(3x + 5) = 12 - (x + 4) \).
3. Solve \( 6x - 3(2x - 4) = 5 + x \).
4. If \( 2(x + 3) = x - 7 \), what is the value of \(x\)?
5. Solve \(7x + 5 = 4x - 8\).

**Tip:** When solving linear equations, always distribute first and then combine like terms to make the equation easier to solve.

Learn how to solve the linear equation 7(3x + 9) = 11 - (x + 3) with a detailed, step-by-step solution. This problem involves key algebraic concepts such as distribution, combining like terms, and solving for x. Suitable for students in Grades 6-8.

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