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Jillana begins to solve a linear equation that results in a variable expression set equal to the same variable expression. Which is the best interpretation of this solution?

A. The equation has one solution: [tex]\( x = 0 \)[/tex].
B. The equation has one solution: [tex]\( x = 1 \)[/tex].
C. The equation has no solution.
D. The equation has infinite solutions.

Sagot :

GinnyAnsweridn
To analyze Jillana's linear equation, consider the following general form for a linear equation:

[tex]\[ ax + b = ax + b \][/tex]

Here, [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\(x\)[/tex] is the variable.

When you simplify this equation, you'll subtract [tex]\(ax + b\)[/tex] from both sides:

[tex]\[ ax + b - (ax + b) = ax + b - (ax + b) \][/tex]
[tex]\[ 0 = 0 \][/tex]

The resulting statement [tex]\( 0 = 0 \)[/tex] is always true, independent of the value of [tex]\(x\)[/tex]. This means that any value for [tex]\(x\)[/tex] will satisfy the original equation.

Therefore, we interpret the equation as having infinitely many solutions, since every value for [tex]\(x\)[/tex] makes the equation true. The best interpretation of this situation is:

The equation has infinite solutions.
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