https://file.aiquickdraw.com/mathbot/file/1726016434930dup5pgnp.jpg

To solve this problem and find the missing number that results in no solutions for the equation, we will go step by step.

The equation is given as:

\[
\text{(missing number)} \cdot x - 11 = -3(-x - 5)
\]

### Step 1: Simplify the right-hand side of the equation.

Distribute the \(-3\) on the right-hand side:

\[
-3(-x - 5) = 3x + 15
\]

Thus, the equation becomes:

\[
(\text{missing number}) \cdot x - 11 = 3x + 15
\]

### Step 2: Identify conditions for "no solutions."

For an equation to have no solutions, it must reduce to a contradiction, like \(k = m\), where \(k\) and \(m\) are different constants. This means the \(x\)-terms on both sides must have the same coefficient but the constants must be different.

Let the missing number be represented as \(a\). Therefore, the equation is:

\[
a \cdot x - 11 = 3x + 15
\]

For the equation to have no solutions, the \(x\)-terms must match. Hence, set the coefficients of \(x\) equal:

\[
a = 3
\]

### Step 3: Check for contradiction.

Now substitute \(a = 3\) into the equation:

\[
3x - 11 = 3x + 15
\]

Next, subtract \(3x\) from both sides:

\[
-11 = 15
\]

This is a contradiction, which means there is no solution.

### Final Answer:
The missing number is **3**.

Would you like further details or have any questions?

### 5 related questions:
1. What is the difference between an equation with no solution and an equation with infinite solutions?
2. How can you determine if an equation has no solutions by just looking at its structure?
3. What are some real-life scenarios where systems of equations have no solutions?
4. How do you handle equations with multiple variables that have no solution?
5. How can you verify whether a solution exists for a given linear equation?

### Tip:
When solving linear equations, look out for the possibility of contradictions (like \(k = m\), where \(k \neq m\)) to identify when an equation has no solutions.

Find the missing number so that the equation has no solutions: (missing number) * x - 11 = -3(-x - 5)

Learn how to find the missing number in the equation (missing number) * x - 11 = -3(-x - 5) so that it has no solutions. This problem covers linear equations, the distributive property, and conditions for no solutions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation