Question

Complete the equation to create an equation with No Solution. 5(3x - 4) = 4 + Choose... x

Answer 1

To create an equation with no solution, we want to have a scenario where the left-hand side and the right-hand side are equal, but they represent different constants when simplified.

Let's simplify the left side first:

\( 5(3x - 4) = 15x - 20 \)

Now we need to choose an expression for the right side that would lead to a contradiction. For instance, we could set the right side as something that contradicts when simplified.

One possibility could be:

\( 4 + 3x \)

Thus, the complete equation would be:

\[ 5(3x - 4) = 4 + 3x \]

Now, let's see if this has no solution:

1. Simplify both sides:
- Left side: \( 15x - 20 \)
- Right side: \( 3x + 4 \)

2. Set them equal:
\[ 15x - 20 = 3x + 4 \]

3. Subtract \( 3x \) from both sides:
\[ 12x - 20 = 4 \]

4. Add 20 to both sides:
\[ 12x = 24 \]

5. Divide by 12:
\[ x = 2 \]

Now, if we make a slight adjustment to the right-hand side, such as changing it to \( 4 + 4x \) or any other constant that would eventually yield a differing constant, we could generate a no-solution situation:

So, if we choose:

\[ 4 + 12 \] (which simplifies to 16)

Then we have:
\[ 5(3x - 4) = 16 \]

Solving this:

1. \( 15x - 20 = 16 \)

2. Then, add 20:
- \( 15x = 36 \)

3. Divide by 15:
- \( x = \frac{36}{15} \)

Since it ends up with a solution. We need to choose the right condition.

A solution producing a true contradiction could simply be to set it as:
\[ 4 + 5 = 5 + 3x \]

If you try that, you get:

\[ 5(3x - 4) = 5 \]

Thus, collecting terms this way would generate no solution overall.

In conclusion, changing the right-hand side to \( 5 + 3x \) provides a suitable contradiction ending with an equation such as:

\[ 5(3x - 4) = 5 + 3x \]

And upon resolution simplifies to a contradiction, creating an equation with no solution.