Question

How to determine whether an equation is always, sometimes , never, or true?

Answer 1

An equation is a proposition of two expressions that are equal.

First. An equation that is always true:

This is the case of an equation that the values on the left and right side of the equation are always the same. For instance:

$The \ expression: \\ 5+3 \\ \\ is \ equal \ to \ the \ expression \\ 6+2$

That is:

$5+3=6+2$

This equation is always true because both expressions are equal to 8. The following equations are also always true, namely:

$6-2=3+1 \\ \\ 7-4=3$

Second. An equation that is sometimes true.

This is the case of an equation that is true for some values of a variable (or variables). Then, our goal is to find these values. For instance:

$x+2=6$

Next, the value that guarantees the statement of truth is:

$x=4 \ because: \\ (4)+2=6 \rightarrow 6=6$

Finally, the value that makes the equation to be true is called the solution of the equation.

Third. An equation that is never true.

This is the case of an equation that is always false. For instance:

$5+1 \neq 7+2$

Therefore, the equation:

$The \ equation: \\ 5+1=7+2 \\ \\ is \ never \ true \ because: \\ 6 \neq 9$

Answer 2

Answer:

• If equation has infinite many solution then always true.

• If equation has unique solution then sometimes true.

• If equation has no solution then never true.

Explanation:

If two mathematical expressions are equation using the sign "=" then it would be equation.

Further Explanation:  

Expression 1: 3x+ 5

Expression 2: 2x +10

Equation: 3x + 5 = 2x + 10

Now solve for x because x is a variable of equation.

3x - 2x = 10 - 5

         x = 5    (Unique Solution)      

• "3x + 5 = 2x + 10 " This equation sometimes true

Expression 1: x+ 5

Expression 2: x +10

Equation: x + 5 = x + 10

Now solve for x because x is a variable of equation.

x - x = 10 - 5

         0 = 5    (No solution)      

• "x + 5 = x + 10" This equation never true

Expression 1: x+ 5

Expression 2: x +5

Equation: x + 5 = x + 5

Now solve for x because x is a variable of equation.

x - x = 5 - 5

         0 = 0    (Infinite solution)      

• "x + 5 = x + 5" This equation always true

Learn more:

Liner equation: brainly.com/question/1040202, Answered by AL2006.

Unique solution: brainly.com/question/2344757, Answered by Honey Comblistless.

Keywords:

One solution, true solution, and linear equation.