Create 2-3 questions that have absolute value in them 2.
1. What is the absolute value of -5?
2. If the absolute value of x is 9, what are the possible values of x?
3. The absolute value of a number is always non-negative.
Sure! Here are two questions that involve absolute value:
1. Solve the equation |3x + 2| = 10 step-by-step.
2. Determine the values of x that satisfy the inequality |x - 4| < 6 step-by-step.
Let me know if you need step-by-step explanations for any of these questions!
Sure! Here are 2-3 questions that involve absolute value:
1. Solve the equation |2x - 5| = 9.
To solve this equation, you need to isolate the absolute value. Split the equation into two cases, one for when the expression inside the absolute value is positive and another for when it is negative. For the positive case, you have 2x - 5 = 9. Solving this gives x = 7. For the negative case, you have 2x - 5 = -9, which gives x = -2. Therefore, the solution to the equation |2x - 5| = 9 is x = -2 and x = 7.
2. If |x - 3| < 2, what are all the possible values of x?
To find the possible values of x, you need to consider two cases: one for when the expression inside the absolute value is positive and another for when it is negative. For the positive case, x - 3 < 2, which gives x < 5. For the negative case, -(x - 3) < 2, which simplifies to x - 3 > -2, and further simplifies to x > 1. Combining these inequalities, the possible values of x are 1 < x < 5.
3. Find the distance between the points (-3, 4) and (1, -2).
The distance between two points in a coordinate plane can be found using the distance formula: d = √[(x2 - x1)^2 + (y2 - y1)^2]. Plugging in the given coordinates, you have d = √[(1 - (-3))^2 + (-2 - 4)^2]. Simplifying this expression gives d = √[16 + 36], which further simplifies to d = √52 or d = 2√13. Therefore, the distance between the points (-3, 4) and (1, -2) is 2√13.