complete the equation so that it has infinite solutions. ( 1 point ) 4 x + 10 = __ x __
To have infinite solutions, the equation needs to be true for any value of "x". In other words, every value of "x" should satisfy the equation.
To achieve this, we can get rid of the "x" variable by subtracting "4x" from both sides of the equation:
4x + 10 - 4x = 0
Simplifying, we have:
10 = 0
However, this equation is never true for any value of "x" since 10 does not equal 0. Therefore, it is not possible to complete the equation so that it has infinite solutions.
To create an equation with infinite solutions, we need to ensure that both sides of the equation are equal regardless of the value of x.
In this case, we can set the two expressions on the right side equal to each other:
4x + 10 = 4x + 10
By doing this, we can see that regardless of the value of x, both sides of the equation will always be equal. Therefore, the equation 4x + 10 = 4x + 10 has infinite solutions.
To complete the equation so that it has infinite solutions, we need to create an equation where both sides are equal regardless of the value of x.
In the given equation, 4x + 10 = __x __, we can see that there is a term missing on the right side of the equation. To make it equal to the left side, we need to add a term that cancels out the x term.
In this case, if we add -4x to both sides of the equation, the x terms on both sides will cancel out:
4x + 10 + (-4x) = __ x __ + (-4x)
(4x + (-4x)) + 10 = __ x __
0x + 10 = __ x __
10 = __ x __
Now, no matter what value we substitute for x, the equation will always hold true because the left side always equals 10, regardless of x. Therefore, the equation 10 = __ x __ has infinite solutions.