Examkin

Soru

Zorluk: OrtaLinear Inequalities in One Variable

A shipping container initially holds 450 packages. A crew unloads the container at a rate of 15 packages per hour, while an automated sorting machine unloads packages at a rate of xx packages per hour. The number of packages remaining in the container after 8 hours must be at most 130. The inequality 450−8(15+x)≤130450 - 8(15 + x) \leq 130 models this scenario. What is the minimum possible value of xx?

Cevap: 25

Cevap

The minimum possible value of xx is 25.
To find the minimum possible value of xx, solve the inequality 450−8(15+x)≤130450 - 8(15 + x) \leq 130. First, distribute the −8-8 to obtain 450−120−8x≤130450 - 120 - 8x \leq 130. Simplify the constant terms on the left side to get 330−8x≤130330 - 8x \leq 130. Subtract 330 from both sides, yielding −8x≤−200-8x \leq -200. Finally, divide both sides by −8-8 and reverse the inequality sign because of the division by a negative number, which results in x≥25x \geq 25. The minimum possible value of xx is 25.

Adım Adım Çözüm

1
Distribute the factor of −8-8 to both terms inside the parentheses.
450−120−8x≤130450 - 120 - 8x \leq 130
To remove the parentheses and prepare to combine like terms.
2
Subtract 120 from 450 to simplify the constants on the left side.
330−8x≤130330 - 8x \leq 130
To simplify the left side of the inequality before isolating the variable.
3
Subtract 330 from both sides of the inequality.
−8x≤−200-8x \leq -200
To isolate the variable term on the left-hand side.
4
Divide both sides by −8-8 and reverse the direction of the inequality symbol.
x≥25x \geq 25
Dividing by a negative value reverses the inequality sign. Since xx must be greater than or equal to 25, the minimum possible value is 25.

Anahtar Kavram

Solving multi-step linear inequalities in one variable, including distributing coefficients and reversing the inequality sign when multiplying or dividing by a negative number.
Bu soruyu puanla

Konular

Linear Inequalities in One Variable

Bu konudan daha fazla soru