Quant test 15

If (x² – 9)/(x – 3) < 0, then x? If (x² – 9)/(x – 3) < 0, then x?

2 Mark(s)

x < 3 x < 3
–3 < x < 3 –3 < x < 3
x > 3 x > 3
All real All real

Solve: (x – 2)(x – 5) ≥ 0. Solve: (x – 2)(x – 5) ≥ 0.

2 Mark(s)

x ≤ 2 or x ≥ 5 x ≤ 2 or x ≥ 5
2 ≤ x ≤ 5 2 ≤ x ≤ 5
x ≥ 2 x ≥ 2
x < 5 x < 5

If (x – 2)(x + 3) < 0, then x? If (x – 2)(x + 3) < 0, then x?

2 Mark(s)

–3 < x < 2 –3 < x < 2
x < –3 x < –3
x > 2 x > 2
|x| < 2 |x| < 2

Solve: (x² – 9)/(x – 2) > 0. Solve: (x² – 9)/(x – 2) > 0.

2 Mark(s)

x < –3 or x > 3, x ≠ 2 x < –3 or x > 3, x ≠ 2
–3 < x < 3 –3 < x < 3
x ≤ –3 x ≤ –3
x ≥ 2 x ≥ 2

If (x² – 25)/(x – 5) ≥ 0, then x? If (x² – 25)/(x – 5) ≥ 0, then x?

2 Mark(s)

x ≤ –5 or x > 5 x ≤ –5 or x > 5
–5 ≤ x < 5 –5 ≤ x < 5
x x

Solve: |x – 2| > 7 Solve: |x – 2| > 7

2 Mark(s)

x – 2 x – 2
> 7. > 7.
x < –5 or x > 9 x < –5 or x > 9
–5 < x < 9 –5 < x < 9

If |3x – 2| ≤ 4, then x? If |3x – 2| ≤ 4, then x?

2 Mark(s)

3x – 2 3x – 2
≤ 4, then x? ≤ 4, then x?
–2/3 ≤ x ≤ 2 –2/3 ≤ x ≤ 2
–2 ≤ x ≤ 2 –2 ≤ x ≤ 2

Solve: |x – 5| ≤ 0 Solve: |x – 5| ≤ 0

2 Mark(s)

x – 5 x – 5
≤ 0. ≤ 0.
x = 5 x = 5
x ≥ 5 x ≥ 5

If x² – 2x – 3 < 0, then x? If x² – 2x – 3 < 0, then x?

2 Mark(s)

–1 < x < 3 –1 < x < 3
x < –1 x < –1
x > 3 x > 3
|x| > 3 |x| > 3

Solve: x² – 2x + 1 > 0. Solve: x² – 2x + 1 > 0.

2 Mark(s)

x ≠ 1 x ≠ 1
x > 1 x > 1
x < 1 x < 1
All x All x

If (x – 5)(x + 1) < 0, then x? If (x – 5)(x + 1) < 0, then x?

2 Mark(s)

–1 < x < 5 –1 < x < 5
x < –1 x < –1
x > 5 x > 5
|x| < 1 |x| < 1

If |2x + 3| ≤ 5, then x? If |2x + 3| ≤ 5, then x?

2 Mark(s)

2x + 3 2x + 3
≤ 5, then x? ≤ 5, then x?
–4 ≤ x ≤ 1 –4 ≤ x ≤ 1
x ≥ –4 x ≥ –4

Solve: 2/(x – 1) > 0. Solve: 2/(x – 1) > 0.

2 Mark(s)

x > 1 x > 1
x < 1 x < 1
x ≠ 1 x ≠ 1
All real x All real x

Solve: (x + 2)(x + 5) > 0. Solve: (x + 2)(x + 5) > 0.

2 Mark(s)

x < –5 or x > –2 x < –5 or x > –2
–5 < x < –2 –5 < x < –2
x ≥ –2 x ≥ –2
x ≤ –5 x ≤ –5

Solve: x² + 2x + 1 ≥ 0. Solve: x² + 2x + 1 ≥ 0.

2 Mark(s)

Always true Always true
Always false Always false
x ≥ 0 x ≥ 0
x ≤ 0 x ≤ 0

Solve: (x – 4)(x – 6) < 0. Solve: (x – 4)(x – 6) < 0.

2 Mark(s)

4 < x < 6 4 < x < 6
x < 4 x < 4
x > 6 x > 6
x ≤ 4 or x ≥ 6 x ≤ 4 or x ≥ 6

Solve: (x² – 16) ≤ 0. Solve: (x² – 16) ≤ 0.

2 Mark(s)

–4 ≤ x ≤ 4 –4 ≤ x ≤ 4
x ≥ 4 x ≥ 4
x ≤ –4 x ≤ –4
|x| ≥ 4 |x| ≥ 4

Solve: |x + 1| < 4. Solve: |x + 1| < 4.

2 Mark(s)

–3 < x < 5 –3 < x < 5
< 4. < 4.
–5 < x < 3 –5 < x < 3
–4 < x < 4 –4 < x < 4

Solve: (x – 2)/(x + 3) ≤ 0. Solve: (x – 2)/(x + 3) ≤ 0.

2 Mark(s)

–3 < x ≤ 2 –3 < x ≤ 2
x ≥ 2 x ≥ 2
x ≤ –3 x ≤ –3
x > –3 x > –3

If |x| ≥ 5, then x? If |x| ≥ 5, then x?

2 Mark(s)

x x
≥ 5, then x? ≥ 5, then x?
x ≥ 5 or x ≤ –5 x ≥ 5 or x ≤ –5
x > –5 x > –5

Solve: x² + 1 > 0. Solve: x² + 1 > 0.

2 Mark(s)

Always true Always true
Always false Always false
Only for x > 0 Only for x > 0
Only for x < 0 Only for x < 0

Solve: (x + 1)(x – 4) > 0. Solve: (x + 1)(x – 4) > 0.

2 Mark(s)

x < –1 or x > 4 x < –1 or x > 4
–1 < x < 4 –1 < x < 4
x ≥ –1 x ≥ –1
x ≤ 4 x ≤ 4

Solve: (x² – 1)(x – 3) < 0. Solve: (x² – 1)(x – 3) < 0.

2 Mark(s)

–1 < x < 1 or x > 3 –1 < x < 1 or x > 3
–∞ < x < –1 or 1 < x < 3 –∞ < x < –1 or 1 < x < 3
x > –1 x > –1
x < 3 x < 3

Solve: (x – 7)² ≤ 0. Solve: (x – 7)² ≤ 0.

2 Mark(s)

x = 7 x = 7
x ≥ 7 x ≥ 7
x ≤ 7 x ≤ 7
All real numbers All real numbers

If (x – 3)² < 0, then solution? If (x – 3)² < 0, then solution?

2 Mark(s)

No solution No solution
x = 3 x = 3
x ≥ 3 x ≥ 3
All real numbers All real numbers

Quant test 15 : Question 1 of 25