How do you solve #(2x1)(x+2)(x4)<=0#?
The inequality holds for
Keep in mind the rule for multiplying:
Combining these rules, you can clearly see that a product of factors is negative if and only if there is an odd number of negative factors (in this case, one or all three).
By signing up, you agree to our Terms of Service and Privacy Policy
To solve the inequality (2x  1)(x + 2)(x  4) ≤ 0, you need to find the intervals on the number line where the expression is less than or equal to zero. This involves identifying the critical points where the expression equals zero and determining the sign of the expression in each interval between these critical points. The critical points occur where each factor equals zero, so:

Set each factor equal to zero:
 2x  1 = 0 ⇒ x = 1/2
 x + 2 = 0 ⇒ x = 2
 x  4 = 0 ⇒ x = 4

Plot these critical points on a number line and divide the line into intervals:
 Interval 1: (∞, 2)
 Interval 2: (2, 1/2)
 Interval 3: (1/2, 4)
 Interval 4: (4, ∞)

Test a value from each interval into the expression (2x  1)(x + 2)(x  4):
 For Interval 1, choose x = 3: () * () * () = 
 For Interval 2, choose x = 0: (+) * (+) * () = 
 For Interval 3, choose x = 3: (+) * (+) * (+) = +
 For Interval 4, choose x = 5: (+) * (+) * (+) = +

Analyze the signs:
 In Interval 1 and Interval 2, the expression is negative or zero, satisfying the inequality.
 In Interval 3 and Interval 4, the expression is positive, not satisfying the inequality.

Combine the intervals where the expression is negative or zero:
 Interval (∞, 2] ∪ [2, 1/2]
Therefore, the solution to the inequality (2x  1)(x + 2)(x  4) ≤ 0 is: x ∈ (∞, 2] ∪ [2, 1/2].
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you solve #2y9>5y+12#?
 How do you graph the inequality #4x2y<3#?
 How do you solve #abs(x+a)<b#?
 How do you solve and write the following in interval notation: #5(52x)≥407x#?
 The graph of g(x) results when the graph of f(x) = x is shifted 6 units upward. Which is the equation of g(x)?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7