Question
Solve the inequality graphically in a two-dimensional plane: x + y < 5
✓
Answer
The given inequality is x + y < 5.
Draw the graph of the line x + y = 5
Table of values satisfying the equation x + y = 5
Draw the graph of the line x + y = 5
Table of values satisfying the equation x + y = 5
| x | 1 | 2 |
| y | 4 | 3 |
Putting (0, 0) in the given in equation we have 0 + 0 < 5 $ \Rightarrow $ 0 < 5 which is true.
$\therefore $ Half plane of x + y < 5 is towards origin.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Show that the three points A(2, 3, 4), B(-1, 2, -3) and C(-4, 1, -10) are collinear and find the ratio in which C divides AB.
The function f is defined by $\begin{equation} f(x)=\left\{\begin{array}{ll} {1-x,} & {x<0} \\ {1} & {, x=0} \\ {x+1,} & {x>0} \end{array}\right. \end{equation}$
Draw the graph of f(x).
→Draw the graph of f(x).
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}\tan\text{x}}{1-\cos\text{x}}$
→Prove that $\lim\limits_{\text{x}\rightarrow\text{a}^+}\ [\text{x}]=[\text{a}]$ for all $\text{a }\in\text{ R}.$ also prove that $\lim\limits_{\text{x}\rightarrow1^-}\ [\text{x}]=0.$
→Prove that: $\cot^2\text{x}-\tan^2\text{x}=4\cot2\text{x}\ \text{cosec}\ 2\text{x}$
→Show the following quadratic equation by factorization method: $\sqrt{2}\text{x}^2+\text{x}+\sqrt{2}=0$
→If $P(n)$ is the statement " $2^n \geq 3 n$ " and if $P(r)$ is true, prove that $P(r+1)$ is true.
→Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse $9x^2 + 4y^2 = 36.$
→Find the derivative of function cosec x cot x.
Two plants A and B of a factory show following results about the number of workers and the wages paid to them:
| Plant A | Plant B | |
|---|---|---|
| No. of workers | 5000 | 6000 |
| Average monthly wages | ₹ 2500 | ₹ 2500 |
| Variance of distribution of wages | 81 | 100 |
In which plant A or B is there greater variability in individual wages?