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Find the student’s error in solving the following inequality.
2 < –3x –4 < 5
6 < –3x < 5
–2 > x > –5/3

The student should have added 4 to all parts (left, middle, and right) to get 6 < –3x < 9.

The student divided 6/–3 incorrectly.

The student should not have switched the direction of the sign in the final step.

Sagot :

Answer:

[tex]-3 < x < -2[/tex]

Step-by-step explanation:

Seperate compound inequalities into system of inequalities: [tex]\left \{ {{-3x-4 > 2} \atop {-3x-4 > 5}} \right.[/tex]

Rearrange unknown terms to the left side of the equation: [tex]-3x > 2+4[/tex]

Calculate the sum or difference: [tex]-3x > 6[/tex]

Reduce the greatest common factor for both sides of the inequality: [tex]-x > 2[/tex]

Divide both sides of the inequality by the coefficient of the variable: [tex]x < -2[/tex]

Rearrange unknown terms to the left side of the equation: [tex]-3x < 5+4[/tex]

Calculate the sum or difference: [tex]-3x < 9[/tex]

Reduce the greatest common factor for both sides of the inequality: [tex]-x < 3[/tex]

Divide both sides of the inequality by the coefficient of the variable: [tex]x > -3[/tex]

Find the intersection: [tex]-3 < x < -2[/tex]

Answer: [tex]-3 < x < -2[/tex]

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