3 5 solving equations with variable on both sides
- 1. Solving Linear Equations Chapter 3
- 2. Steps to Solving Equations Change subtraction to plus a negative. Remove all grouping symbols and/or exponents (distribute). Combine like terms on the same side of the equal sign. Get all variables on the same side of the equation (move the smallest). Find the variable.
- 3. Steps to Solving Equations (cont’d) Find the farthest thing from the variable on the same side of the equation. Determine how it is attached. Figure out the opposite operation to remove it. Do the opposite operation on both sides of the equation. Repeat these steps until the variable is isolated.
- 4. Special Cases No solution: there is no value for the variable that will solve the equation. Results in a false statement Infinite solutions: all values for the variable will solve the equation. Results in a true statement
- 5. Solve: 6 – b = 5 b + 30 b = -4 b = 4 b = -6 b = 6 None of the above
- 6. Solve: 12 x + 43 = 21 – 10 x x = 16/3 x = 1 x = -1 x = -37/6 None of the above
- 7. Solve: s = 44/5 s = 11 s = 44 s = 11/6 None of the above
- 8. Solve: y = -90 y = 10 y = -21 Infinite solutions None of the above
- 9. Solve: 5 y – 2 y = 3 y + 2 y = -2/6 y = 2/6 y = -1/3 No solution None of the above
- 10. Solve: 3( a + 1) – 5 = 3 a – 2 a = 8/6 a = 4/3 No solution Infinite solutions None of the above
- 11. Solve: 2(7 + 3 t ) = - t t = 14/5 t = -14/5 t = 2 t = -2 None of the above
- 12. Solve: –3( x + 5) = 3( x – 1) x = 2 x = -2 x = 3 No solution None of the above
- 13. Which of the following equations is false for all values of m ? 5 + 2 m = 5(–4 + 2 m ) 5 + 10 m = 5(–4 + 2 m ) 20 + 2 m = 5(–4 + 2 m ) -20 + 10 m = 5(–4 + 2 m ) None of the above
- 14. Ken and Maggie are feeding their dogs. They start with an equal number of bones. Ken fed 4 dogs and had one bone left. Maggie fed 2 dogs and had five bones left. How many bones did each dog get? 1 2 3 4
- 15. Travis and Bill earn the same hourly pay. One week their paychecks were equal, but Bill worked 26 hours and Travis worked 18. Travis got a $50 bonus for overall good work attendance. How much total did each person earn that week? $6.25 $94 $162.50 $212.50 None of the above