The expression on the left side of an equation is shown below. $$ \begin{array}{l}3 x+9=\square \ ext { If the equation has no solution, which expression can be written in the box on the other side of the equation? } \ -9 \ -3 \ 3 x \ 3 x+9\end{array} $$

Question

The expression on the left side of an equation is shown below. $$ \begin{array}{l}3 x+9=\square \ 	ext { If the equation has no solution, which expression can be written in the box on the other side of the equation? } \ -9 \ -3 \ 3 x \ 3 x+9\end{array} $$

UpStudy AI · Accepted Answer

To determine which expression can be placed in the box such that the equation $$3x + 9 = \square$$ has no solution, we need to analyze the conditions under which an equation has no solution.

An equation has no solution when the left side and the right side cannot be equal for any value of $$x$$. This typically occurs when the two sides represent parallel lines in a linear equation context, meaning they have the same slope but different y-intercepts.

Let's analyze the options provided:

1. **Option -9**: 
   - The equation would be $$3x + 9 = -9$$.
   - Rearranging gives $$3x = -18$$, which has a solution $$x = -6$$. So, this option does not lead to no solution.

2. **Option -3**: 
   - The equation would be $$3x + 9 = -3$$.
   - Rearranging gives $$3x = -12$$, which has a solution $$x = -4$$. So, this option does not lead to no solution.

3. **Option $$3x$$**: 
   - The equation would be $$3x + 9 = 3x$$.
   - Rearranging gives $$9 = 0$$, which is a contradiction. This means there is no value of $$x$$ that can satisfy this equation. Thus, this option leads to no solution.

4. **Option $$3x + 9$$**: 
   - The equation would be $$3x + 9 = 3x + 9$$.
   - This is always true for any value of $$x$$, meaning it has infinitely many solutions. So, this option does not lead to no solution.

Based on this analysis, the expression that can be written in the box such that the equation has no solution is:

**$$3x$$**.
The expression that makes the equation $$3x + 9 = \square$$ have no solution is $$3x$$.

The expression on the left side of an equation is shown below. \( \begin{array}{l}3 x+9=\square \\ \text { If the equation has no solution, which expression can be written in the box on the other side of the equation? } \\ -9 \\ -3 \\ 3 x \\ 3 x+9\end{array} \)

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions