Problem Solving with Inequalities
Algebra, and more...
 
1. EASY

Solve \(3x-5 > 7\)

 
2. EASY

Solve \(7-2x < -3\)

 
3. MEDIUM

Given \( a > b > c > d \), which of the following must be true?

  1. \(a-b>c-d\)
  2. \(ab>cd\)
  3. \(a+c>b+d\)
  4. \(\frac{a}{d}>\frac{c}{b}\)
  5. \(a+b>c+d\)
 
4. MEDIUM

If \((x-3)^2 > (x-3)^3\) and \((x-3)^3\le0\), which of the following is the most accurate range for x?

  1. \(x>3\)
  2. \(x\ge3\)
  3. \(x=3\)
  4. \(x\le3\)
  5. \(x<3\)
 
5. HARD

Given \(a>b>c>d>0\), which of the following is the greatest?

  1. \(\frac{a}{d}\)
  2. \(\frac{c}{b}\)
  3. \(\frac{c}{d}\)
  4. \(\frac{a}{b}\)
  5. \(\frac{d}{a}\)
 
6. HARD

Solve \(3x^2-3 > 2x^2+2x\)

 
7. HARD

Solve \(2x-4 < 3x+7 < x+1\)

 
8. HARD

Solve \(x^4 > x^3\)

 
9. HARD

Solve \(x^4+x < x^3+x^2\)

 
10. HARD

Solve for \(x\) where \(4x < 16\) and \(-3x < -6\)