Complete the equation so that it has infinite solutions.

Question

4x + 10 =____ x+____

GPT-4o mini · Answer

To make the equation $4x + 10 = ax + b$ have infinite solutions, both sides of the equation must be equivalent. This means the coefficients of $x$ and the constant terms must be equal. Starting from: $$ 4x + 10 = ax + b $$ For the coefficients of $x$: $$ 4 = a $$ For the constant terms: $$ 10 = b $$ Thus, substituting these values into the equation, we have: $$ 4x + 10 = 4x + 10 $$ So, the completed equation is: $$ 4x + 10 = 4x + 10 $$ This will have infinite solutions since both sides of the equation are identical.

Just-A-V3nter · Answer

Complete the equation so that it has no solution. 5x + 12 = ____x + 9

GPT-4o mini · Answer

To make the equation $5x + 12 = ax + 9$ have no solutions, the coefficients of $x$ must be equal, but the constant terms must be different. Starting with: $$ 5x + 12 = ax + 9 $$ To ensure the coefficients of $x$ are the same: $$ a = 5 $$ Now, for the constant terms, we need them to be different: $$ 12 \neq 9 $$ Thus, substituting $a$ into the equation and keeping the constant different, we have: $$ 5x + 12 = 5x + 9 $$ This will result in: $$ 12 \neq 9 $$ So, the completed equation is: $$ 5x + 12 = 5x + 9 $$ This will have no solution since both sides have the same coefficient of $x$, but the constant terms differ.

Just-A-V3nter · Answer

Complete the equation so that it has no solution. −7x − 12 = _____x + 12

GPT-4o mini · Answer

To create an equation that has no solution with the given expression $-7x - 12 = ax + 12$, we need to ensure that the coefficient of $x$ on both sides of the equation is the same while ensuring that the constant terms are different.

From your equation:

\[ -7x - 12 = ax + 12 \]

For the coefficients of $x$: \[ a = -7 \]

Now, for the constant terms, we need them to be different. The left side has $-12$ and the right side has $12$, which are already different.

Thus, substituting $a$ into the equation, we have:

\[ -7x - 12 = -7x + 12 \]

This will result in:

\[ -12 \neq 12 \]

So the completed equation is:

\[ -7x - 12 = -7x + 12 \]

This equation has no solution because both sides have the same coefficient for $x$, but the constant terms are different.