Grade 9 Mathematics Quiz: Solving Multi-Step Inequalities
Instructions: Below are questions regarding the topic of solving multi-step inequalities. Each question includes multiple choice answers. Only one answer is correct. Read each question carefully and choose the best option.
- Question 1
The image of a number line with arrows indicating the region to the right of -3, shaded lightly. An inequality is written as x > -3.
What is the solution to the inequality ( 2x - 4 > 2 )?
A. ( x > 3 )
B. ( x < 3 )
C. ( x > 2 )
D. ( x < 2 )
- Question 2
The image of a graph showing a shaded region below the line y = 2x + 1, with a dashed line.
What is the result of solving the inequality ( -3x + 2 < 5 )?
A. ( x > -1 )
B. ( x < -1 )
C. ( x > 1 )
D. ( x < 1 )
- Question 3
The image of a shaded area on a coordinate graph where x is greater than or equal to 0 and y is less than 4.
Determine the solution to the compound inequality ( 5 \leq x + 6 < 10 ).
A. ( -1 < x < 4 )
B. ( -11 < x < 4 )
C. ( -1 < x < 5 )
D. ( -1 \leq x < 4 )
- Question 4
The image of two parallel lines on a coordinate plane. One above the other, with the upper line y = 3 and the lower line y = x + 1, showing the area between them shaded.
Solve the inequality ( 4x - 9 ≤ 3 ).
A. ( x ≥ 3 )
B. ( x < 3 )
C. ( x ≤ 3 )
D. ( x > -3 )
- Question 5
The image of a graph representing a quadratic function that opens upwards, with a shaded region below the parabola. The vertex of the parabola appears at the point (1, -3).
What is the solution to the inequality ( x^2 - 2x - 3 < 0 )?
A. ( 1 < x < 3 )
B. ( -1 < x < 3 )
C. ( x < 1 )
D. ( x > 3 )
Answer Key
- A. ( x > 3 )
- B. ( x < -1 )
- D. ( -1 \leq x < 4 )
- C. ( x ≤ 3 )
- A. ( 1 < x < 3 )
Check each solution accurately corresponds to the inequalities presented in the questions.