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Chapter Summary and Review continued 3.3 Examples on pp. 144–146 SOLVING MULTI-STEP EQUATIONS EXAMPLE You may need more than one step to solve an equation. 2p (5) 2p 13 Write original equation. 2p 5 2p 13 Use subtraction rule to simplify. 4p 5 13 Combine like terms 2p and 2p. 4p 5 5 13 5 Subtract 5 from each side to undo the addition. 4p 8 Simplify both sides. 4p 8 4 4 Divide each side by 4 to undo the multiplication. p 2 Simplify. Solve the equation. 7. 26 9x 1 8. 32 4c 12 10. 2(4 x) 7 5 3.4 11. n 3(1 2n) 17 9. 9r 2 6r 1 3 12. (x 8) 9 4 Examples on pp. 151–153 SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES EXAMPLES Linear equations can have one solution, no solution, or many solutions. To solve, collect the variable terms on one side of the equation. Equation with one solution: Equation with no solution: Equation with many solutions: 15d 20 7d 4 6x 5 15 6x 2n 5n 11 2 3n 9 8d 24 6x 5 6x 15 6x 6x 3n 11 11 3n d 3 5 15 The solution is 3. The original equation has one solution. 5 15 is never true no matter what the value of x. The original equation has no solution. 11 11 11 11 is always true, so all values of n are solutions. The original equation is an identity. Solve the equation if possible. Determine whether the equation has one solution, no solution, or is an identity. 190 13. 24 3x 9x 14. 15x 23 15x 15. 2m 9 6 m 16. 36 4d 4(9 d) 17. 12 11h 18 4h 18. 2x 18 4x 2x 10 Chapter 3 Solving Linear Equations