Question

the value of ( x ) is decreased by 78%. which expression does not represent this situation?
answer
( (1 - 0.78)x ) ( 0.22x )
( 1x - 0.78x ) ( 0.78x )

Explanation:

Step1: Analyze the meaning of decreasing by 78%

When a value \( x \) is decreased by 78%, we first find the remaining percentage. The remaining percentage is \( 100\% - 78\%=22\% = 0.22 \) in decimal. So the new value can be expressed as \( x-0.78x=(1 - 0.78)x = 0.22x \).

Step2: Analyze each option

• Option \((1 - 0.78)x\): This is equivalent to \( x-0.78x \), which represents the value of \( x \) decreased by 78%, because we are taking 78% (0.78) of \( x \) away from \( x \).
• Option \(0.22x\): Since \( 1- 0.78 = 0.22 \), this is the same as \((1 - 0.78)x\), so it represents the value of \( x \) decreased by 78%.
• Option \(1x-0.78x\): This is the direct way of subtracting 78% of \( x \) from \( x \), so it represents the value of \( x \) decreased by 78%.
• Option \(0.78x\): This represents 78% of \( x \), not the value of \( x \) decreased by 78%. Decreasing by 78% means we keep 22% of \( x \), not take 78% of \( x \).

Answer:

\( 0.78x \)