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Linear Equations

Linear Equations

Lesheey
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Linear Equations

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  1. Linear Equations and Inequalities 

  2. Definition of Linear EquationsLinear equation — an equation in which each variable appears only to the first power, and the graph of the equation represents a straight line in a Cartesian coordinate plane.General form:ax + b = 0or in multiple variables:a₁x₁ + a₂x₂ + … + aₙxₙ = bwhere aᵢ and b are constants, and at least one aᵢ ≠ 0.

  3. Strategy.To solve a linear equation, the general strategy is to isolate the variable by simplifying both sides of the equation and then performing inverse operations to get the variable by itself. Finally, check the solution by substituting it back into the original equation.

  4. Level 1. Form: ax = b 3x=6

  5. Level 2. Form: ax+b=c 8x+6=30

  6. Level 3. Form: ax = b + cx 4x=12 + 2x

  7. Level 4. Form: a(x + b) = c 3(x+3)=18

  8. Level 5. Form: a(bx+c)=d(ex+f) 5(2x+4)= 3(4x-10)

  9. Level 6. Form: = b, x ≠ 0 = 5

  10. Linear InequalitiesA linear inequality is an inequality that involves a linear expression in one or more variables.It shows the relationship between expressions using inequality symbols such as <, >, ≤, or ≥, instead of an equal sign.

  11. Strategy.The strategy for solving linear inequalities is similar to the strategy for solving linear equations. The only thing to note is that if we multiply or divide both sides of the inequality by a negative number, we must reverse the inequality sign.

  12. Level 1. Form: ax < b 3x>12

  13. Level 2. Form: ax ≤ b 7x≤14

  14. Level 3. Form: ax<b+cx 4x<12 + 6x

  15. Level 4. Form: ax ≥ b+cx 2x≥16 + 6x

  16. Level 5. Form: a≥b+cx>d 4≥2x+5>-3

  17. Activity 1.Wachiravit is playing his favorite zombie shooting game in Roblox. From previous levels, he has saved up 160 Robux, which he decided to spend on buying a new gun and ammunition for it. The gun costs 70 Robux, and one bullet costs 3 Robux. How many bullets can he buy?

  18. Activity 2.Nutcha is playing Dota 2 with her friends as a position 5 support. Her team is planning to attack, and she needs to buff her teammates with the "Blood Lust" spell. Her character has 650 mana, but she needs to save 350 mana to cast her ultimate during the fight. How many teammates can Nutcha buff if the cost of casting "Blood Lust" is 120 mana?

  19. Activity 3. 5y−8=2y+13

  20. Activity 4. 5y−8=2y+13

  21. Activity 4. 0.5x−1.2=3.8

  22. Activity 5. 6(a+2)−4=14

  23. Activity 6. 7−3m≥10

  24. Activity 7. 6(𝑎+2)−4≤14

  25. Activity 8. −2x+9>3

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