&âś“ The operations that can be used to solve the
& equation are addition and multiplication.
&* The operations that can be used to solve the
& equation are multiplication and division.
&* The equation has infinitely many solutions.
&* The equation has a solution ofx=53.
&âś“ The equation has no solutions.
Practice makes perfect
We are asked to select all statements that apply to the equation 10x+45x-13=5(11x+6).
& The operations that can be used to solve the
& equation are addition and multiplication.
& The operations that can be used to solve the
& equation are multiplication and division.
& The equation has infinitely many solutions.
& The equation has a solution ofx=53.
& The equation has no solutions.
First, let's try to solve the given equation.
Notice that we can now stop solving the equation because any number (for example, 55x) cannot be equal to the same number (55x) after adding 66.
55x-13≠55x+66
Therefore, the given equation has no solutions. We can already select one of the options from the list.
& The operations that can be used to solve the
& equation are addition and multiplication.
& The operations that can be used to solve the
& equation are multiplication and division.
& The equation has infinitely many solutions.
& The equation has a solution ofx=53.
&âś“ The equation has no solutions.
Since the equation has no solutions, it does not have a solution of x=53. Also, the equation cannot have infinitely many solutions if it does not even have one solution.
& The operations that can be used to solve the
& equation are addition and multiplication.
& The operations that can be used to solve the
& equation are multiplication and division.
&* The equation has infinitely many solutions.
&* The equation has a solution ofx=53.
&âś“ The equation has no solutions.
To solve the equation, we used only addition and multiplication. Therefore, we will select the first option.
&âś“ The operations that can be used to solve the
& equation are addition and multiplication.
& The operations that can be used to solve the
& equation are multiplication and division.
&* The equation has infinitely many solutions.
&* The equation has a solution ofx=53.
&âś“ The equation has no solutions.
Finally, we will decide if we want to select the second option. In the last step of solving the equation we had to combine the x-terms on the left-hand side of the equation using addition.
10x+45x-13=55x+66
⇕
55x-13=55x+66
This was necessary to clearly see that the equation has no solutions. Therefore, this equation cannot be solved using only multiplication and division — we also need addition. Because of this, we will not select the second option.
&âś“ The operations that can be used to solve the
& equation are addition and multiplication.
&* The operations that can be used to solve the
& equation are multiplication and division.
&* The equation has infinitely many solutions.
&* The equation has a solution ofx=53.
&âś“ The equation has no solutions.
