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One-Step Linear Equations: Solve with Whole Number Coefficients

Learn to solve one-step linear equations with positive rational solutions involving whole number coefficients. Understand key terms like variable, coefficient, and equation. Practice using inverse operations to isolate the variable and balance expressions.

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One-Step Linear Equations: Solve with Whole Number Coefficients

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  1. 6.18 The students will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions.

  2. 6.18 VocabularyPg Variable- A variable is a symbol (placeholder) used to represent an unknown numerical value. A letter is typically used to represent unknown numbers (Ex. x or y). Term- A term is a number, variable, product, or quotient in an expression or equation. For example, in 2x + 18, there are two terms, 2x and 18. Expression-One side of an equation; in the equation 16 + 6= 22, there are two expressions, 16 + 6 and 22. Coefficient- A coefficient is the numerical factor in a term. For example, in the term 3x, 3 is the coefficient; in the term x, 1 is the coefficient. Equation- An equation is a mathematical sentence that states the two sides, separated by an equal sign, are equal. HAS AN EQUAL SIGN!!! Algebra- A mathematical language that uses symbols, usually letters that stand for unknowns, along with numbers. The word algebra is a Latin variant of the Arabic word al-jabr, describing how to solve an equation Inverse Operation- The process in which an opposite of a term is used to cancel it out. For example- 4y means 4 times y = 12, so use the opposite, or INVERSE, operation on both sides of the equation (inverse of multiplication is division) 4y=12 4 4 (fractions are division) y=3 • Pg 6.18 Practice • Directions for inverse operation • The name of the game is to get the variable by itself on one side of the equation ….x=8 • Do the inverse operation on both sides of the equation to cancel terms to get the variable alone. (variables are letters) • 5r is multiplication (5 • r), the inverse is division. • (fractions) are division, the inverse is multiplication • Addition’s inverse is subtraction Subtraction’s inverse is addition • Practice- • 1) 4 + x = 10 2) y - 5= 3 3) 35 = 7z 4. = 30 • Try on your own! • 5) w – 3 = 2 6) k + 4 = 3 7) e – 14 = 19 • 9) a + 4 = 1 10) j – 11 = 14 11) = 10

  3. Remember, The Variable Wants To Be Alone!!!!!!! = 4 + 3 = 7

  4. Practice with Algebra Representations • You will be given illustrations and must be able to determine the terms, variables, operations, and answer for the variable. • WHAT YOU DO TO ONE SIDE YOU MUST DO THE SAME THING TO THE OTHER SIDE!!!!!!!! • THE EXPRESSIONS MUST BALANCE!

  5. = Solve for x when = X and = 1Write the values above each picture.= 6 2x = = = = = =

  6. Solve for T when = T and = 1Write the values above each picture. Hi! I’m Mr. Equal!

  7. Solve for C when C= and 1= Write the values above each picture.

  8. Solve for X when X= and 1= Write the values above each picture = X + 8 16 I WANT TO BE ALONE! X + 8 = 16 Or…… X= 8 -8 -8 X= 8

  9. Your Turn!!!!!!!

  10. 1. = = x = 1

  11. 2. = x = 1

  12. 3. In the equation 3x=6 how many terms are there?

  13. 4. In the equation 3+ x =6 how many terms are there?

  14. 5. In the equation 3x=6 what is the co-efficient?

  15. 6. In the equation 3x=6 what is the variable?

  16. 7. Solve using inverse operationz + 52 = 93

  17. 8. Solve using inverse operation7m = 126

  18. 9. Solve using inverse operation15 = 3 + x

  19. 10. Solve using inverse operation⅙ = 3 x

  20. 11. = = x = 1

  21. 12. = = x = 1

  22. 13. = = x = 1

  23. 14. 8x=104

  24. 15. x - 18 = 100

  25. EXIT TICKET 6.18 1. How many Terms in 4x=12?2. What is the variable in 4x=12?3. What is the co-efficient in 4x=12?4. Solve USING INVERSE OPERATION4x=125. Solve USING INVERSE OPERATIONx + 4 =12

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