# Tagged Questions

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### solving the system

solve the system : $$y+|x-2|=3$$, $$|x+y|= m$$ graphicly when $m$ equals $6$. I can easily (realtively) skecth the first graph , however, how the bloody hell do you sketch $|x+y|= 6$??
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### inequality method of solution

Im looking for an efficent method of solving the following inequality: $$\left(\frac{x-3}{x+1}\right)^2-7 \left|\frac{x-3}{x+1}\right|+ 10 <0$$ I've tried first determining when the absolute value ...
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### Absolute value on a number line

Solve : |x-4|>a if case1:a>0 and case2:a<0 I am getting answers which look similar in both cases. please i wish to know why it is so and how different both answers are when plotted on a number ...
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### Absolute value of a real number

My question is: Solve: $|x-4|< a$, where $a$ belongs to the real numbers. Solve this by considering various cases depending upon whether $a$ is negative, positive or zero. What I have tried ...
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### How to minimize an equation with absolute values?

How would I go about minimizing the expression $\left(|z_1| + |z_2|\right) \times \left(|z_1 + z_2| + |z_1 - z_2|\right)$ subject to the constraint $|z_1|^2 + |z_2|^2 = 1$ given that $z_1$ and ...
### Prove by contradiction or contrapositive? If $|x+y|<|x|+|y|$, then $x<0$ or $y<0$.
Prove: If $|x+y|<|x|+|y|$, then $x<0$ or $y<0$ This looks as though it's true from the start. Take $x=-4, y=4$. $|-4+4|<|-4|+|4|$ $0<8$ is true. The question is asking for a ...