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Complete the equation so that it has infinite solutions

4x+10=__ x+ ___

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
3 days ago

To create an equation with infinite solutions, both sides of the equation must be equivalent for all values of \( x \). This means the left side must be a multiple of the right side.

We can rewrite the left side of your equation:

\[ 4x + 10 \]

Now we want the right side to be equivalent to this. If we set:

\[ \_\_ = 4 \] (to match the coefficient of \( x \))

and

\[ \_\_ = 10 \] (to match the constant term),

then we can write:

\[ 4x + 10 = 4x + 10 \]

So, filling in the blanks, the completed equation for infinite solutions is:

\[ 4x + 10 = 4x + 10 \]

User Icon for UnicornSparkles UnicornSparkles answered
3 days ago

Complete the equation so that it has no solution.(1 point)

5x+12=___ x+9

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
3 days ago

To create an equation that has no solutions, the left side and right side must be parallel lines that never intersect. This typically happens when the coefficients of \(x\) are the same but the constant terms are different.

Given the left side:

\[ 5x + 12 \]

To have no solution, we can match the coefficient of \(x\) and set a different constant. For example, we can set:

\[ \_\_ = 5 \] (matching the coefficient of \( x \))

And for the constant, we should choose a value that is different from \( 12 \). Let's choose \( 10 \):

So, the right side would be:

\[ 5x + 10 \]

Thus, the completed equation that has no solution is:

\[ 5x + 12 = 5x + 10 \]

This equation has no solutions because \( 5x + 12 \) and \( 5x + 10 \) represent parallel lines.