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Inequalities Question (1 Viewer)
- Thread starter pikachu975
- Start date
Hint: the given inequality with the absolute values says that the distance of x from -2 plus its distance from 3 is equal to 5. This clearly happens when and only when x lies between -2 and 3 (inclusive).
The answer is C.
You can picture |x+2| + |x-3| = 5 on a number line. x+2 simply means the value of x being shifted 2 units to the left of the origin, and x-3 means the value of x being shifted 3 units to the right of the origin.
You should immediately tell that the parabola x^2 - x -6 ≤ 0 has roots -2 and 3. Graph the parabola and you will see that the parabola is ≤ 0 when -2 ≤ x ≤ 3, which has the same solution as your original equation.
You can picture |x+2| + |x-3| = 5 on a number line. x+2 simply means the value of x being shifted 2 units to the left of the origin, and x-3 means the value of x being shifted 3 units to the right of the origin.
You should immediately tell that the parabola x^2 - x -6 ≤ 0 has roots -2 and 3. Graph the parabola and you will see that the parabola is ≤ 0 when -2 ≤ x ≤ 3, which has the same solution as your original equation.