Draw the graph of the inequation x + y ≤ 0 .

To graph the inequality x + y ≤ 0 , you can follow these steps: 1. Begin by recognising that this is a linear inequality in two variables, x and y , and it represents a half-plane. 2. Start by graphing the boundary line x + y = 0 , which is a straight line passing through the origin ( 0 , 0 ) and has a slope of - 1 . You can find two points on this line easily: ( 0 , 0 ) and ( 1 , - 1 ) . Connect these two points to draw the line. 3. Determine which side of the line to shade. Since the inequality is x + y ≤ 0 , you want to shade the region where x + y is less than or equal to 0. This means you should shade the area below the line. 4. Shade the area below the line, including the line itself, to represent the solution to the inequality x + y ≤ 0 . Here's a rough sketch of the graph: The shaded region below and including the line x + y = 0 represents the solution to the inequality x + y ≤ 0 .

Solve: 36 x - 7 2 + 3 x ≥ 1 2

We have to solve: 36 x - 7 2 + 3 x ≥ 1 2 Transpose the denominator to other side and make it in form of linear inequation. ⇒ 72 x - 14 ≥ 2 + 3 x ⇒ 72 x - 3 x ≥ 2 + 14 ⇒ 69 x ≥ 16 ⇒ x ≥ 16 69 Hence, the required answer is x ≥ 16 69 .

E M B I B E

Pearson IIT Foundation Mathematics Class 8>Chapter 11 - Linear Equations>PRACTICE QUESTIONS CLASSROOM WING>Q 30

EASY

8th Foundation

IMPORTANT

Earn 100

The sum of three consecutive even numbers is $72$ . Find the numbers.

Important Questions on Linear Equations

EASY

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 11 - Linear Equations>PRACTICE QUESTIONS CLASSROOM WING>Q 31

Rahul is $7$ years older than Ramu. The ratio of their ages is $4 : 3$ . Find their ages

EASY

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 11 - Linear Equations>PRACTICE QUESTIONS CLASSROOM WING>Q 32

Solve $a + 2 b = 4$ and $2 a + b = 9$

EASY

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 11 - Linear Equations>PRACTICE QUESTIONS CLASSROOM WING>Q 33

The cost of $3$ Maths books and $4$ Physics books is $₹ 31$ , whereas that of $4$ Maths books and $3$ Physics books is $₹ 32$ . Find the cost of $5$ Maths books and $4$ Physics books.

EASY

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 11 - Linear Equations>PRACTICE QUESTIONS CLASSROOM WING>Q 34

How much pure milk be added to a six litres of $60 %$ milk solution so that the resultant solution contains $80 %$ milk?

EASY

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 11 - Linear Equations>PRACTICE QUESTIONS CLASSROOM WING>Q 35

Solve for $x : \frac{3}{2} (7 - \frac{4 x}{3}) - \frac{3}{5} (\frac{x}{3} - \frac{2}{3}) + \frac{6}{5} (\frac{2 x}{3} - \frac{7}{2}) = \frac{3 x}{2} - \frac{8}{5}$

EASY

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 11 - Linear Equations>PRACTICE QUESTIONS CLASSROOM WING>Q 37

Draw the graph of the inequation $x + y \leq 0$ .

EASY

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 11 - Linear Equations>PRACTICE QUESTIONS CLASSROOM WING>Q 38

Shiva can type $x$ words per hour, whereas Sreenivas can type $y$ words per hour. Shiva works for $5 h r$ per day and Sreenivas works for $7 h r$ per day. If both can type at least $700$ words in a day, then frame an inequation to support the above data.