Complete Equation With No Solutions Or Infinitely Many Solutions Worksheet

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In algebra, an equation with no solutions means that there is no value that satisfies the equation. On the other hand, an equation with infinitely many solutions means that any value of the variable satisfies the equation.

For Example:

`i)` Find the missing number so that the equation has infinitely many solutions.

$5x-3=5x+ \square$

`ii)` Find the missing number so that the equation has no solutions.

$2x+7=\square \, x-19$

Algebra 1

One-Variable Equations

How Will This Worksheet on "Complete Equation with No Solutions or Infinitely Many Solutions" Benefit Your Students' Learning?

Students can spot inconsistencies in mathematical expressions by knowing when an equation has no solutions.
Examining equations that have an infinite number of solutions pushes students to think through different scenarios, which enhances critical thinking.
Understanding equations that have no or infinite solutions helps to emphasize how crucial accuracy and clarity are when solving mathematical problems.
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Solved Example

Q. Find the missing number so that the equation has infinitely many solutions.

\newline

-3x - 10 = -3x + \underline{\hspace{1cm}}

Solution:

Infinitely many solutions: When does this equation have infinitely many solutions? Infinitely many solutions occur when the both sides of the equation are identical.
Identical sides: -3x - 10 = -3x + ____ $\newline$ To have infinitely many solutions, the constants on both sides must also be the same.
Matching constants: The constant on the left side is $-10$ . For the equation to have infinitely many solutions, the constant on the right side must also be $-10$ .
Determining missing number: Therefore, the missing number in the equation is $-10$ . $\newline$ $-3x - 10 = -3x - 10$