Grade 8 One Variable Linear Equations and In-Equations Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) in Each Question, Write in the Missing Statement or Equation

(a)

(b)

(2) Solve Each Equation. Then Represent the Solution on the Number Line

(a)

(b)

(3) Solve below Equation

(a)

(4) Solve below Equation

(a)

(5) Solve below Equation

(a)

(6) Solve below Equation

(a)

(7) from ABC City Six More Than One Fourth of the Total Number of Student Select Science Stream. Two More Than One Half of the Student Select Commerce Stream, Remaining 100 Student Select Arts Stream. Find Total Number of Student in the City

(8) Write in the Solution Set for Each of the Given In-Equation. Then Represent Each Solution Set on the Number Line. Note: Solution Set is the Set of Values That Satisfies an In-Equation

(a) Find the Values of x that are natural number and satisfy the in-equation

(9) Write in the Solution Set for Each of the Given In-Equation. Then Represent Each Solution Set on the Number Line. Note: Solution Set is the Set of Values That Satisfies an In-Equation

(a) Find the values of x that are integer and satisfy the in-equation,

(10) Write in the Solution Set for the Given Equation

(a)

(11) Solve Each Equation

(a)

(b)

(12) Solve the In-Equation. Than Represent the Solution Set on the Number Line

(a)

Answers and Explanations

Answer 1 (A)

  • Twenty times a number added by 120 equals 400.
  • To find out its equation will go step by step

(i) Twenty times a number (Suppose Number is ā€œaā€ )

(ii) Added by 120

(iii) Equals 400

  • So, missing equation,

Answer 1 (B)

  • To find out its equation will go step by step.

(i)

(ii)

(iii)

  • So, missing Statement is:

Answer 2 (A)

  • Given equation,

  • Now taking the unknown left side and number to right side,

  • Representation of number on line is as below,
Illustration 2 for Answers_and_Explanations

Answer 2 (B)

  • Given equation

  • Now taking the unknown left side and number to right side,

Illustration 3 for Answers_and_Explanations

Answer 3 (A)

  • Given equation,

  • Now taking the unknown left side and number to right side,

Answer 4 (A)

  • Given equation,

  • Now take LCF on left hand side and right hand side separately.

Answer 5 (A)

  • Now take LCF on left hand side and right hand side separately.

Answer 6 (A)

  • Now taking the unknown left side and number to right side,

Answer (7)

  • Suppose total number of student in the ABC city
  • Six more than one fourth of the total numbers of student select the science.
  • So,

  • Two more than one half of the total student select commerce.

  • Remaining 100 student select Arts Stream
  • Now,

  • Therefore, total number of student in the ABC city is

Answer 8 (A)

  • Natural number are the positive integer or nonnegative integer which starts from 1 and ends at infinity such as

  • So, from above the values of x are such that,

  • Means values of x are less than four that means
  • So, Solution Set is
  • Representation on number line is as below
Illustration 4 for Answers_and_Explanations

Answer 9 (A)

  • Integer: An integer ia s whole number that can be positive, negative or zero.
  • For example;

  • But rational number and decimal number like is not an integer.
  • The values of x that satisfy In-equation are,

  • Representation on number line is as below,
Illustration 5 for Answers_and_Explanations

Answer 10 (A)

  • Here first solution set of x is only belongs to N means,
  • ā€œNā€ -means natural number; means numbers are the positive integer or nonnegative integer and start from 1 and end at infinity.
  • Solving the given equation,

  • So, solution set of value of x is
  • Representation of Solution set of value x on number line is as below.
Illustration 6 for Answers_and_Explanations

Answer 11 (A)

  • Given equation,

Answer 11 (B)

  • Given equation,

Answer 12 (A)

  • Now, , Z means integer , that means the whole positive number , whole negative number, and Zero.
  • So, Solution Set of value x is;

  • Representation of Solution set of value x on number line is as below.
Illustration 7 for Answers_and_Explanations

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