Solving Algebraic Equations
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- Eleanore Owens
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1 Lesson 4. Solving Algebraic Equations Add 3 to both sides. Divide both sides by. 4 gives the solution of the equation 3. Check: Substitute 4 for x into the original equation When 4, the equation 3 is true. So gives the correct solution Subtract from both sides. 8 8 Divide both sides by. gives the solution of the equation Check: Substitute for x into the original equation When, the equation is. So gives the solution. 9 Chapter 4 Lesson 4.
2 y 0 Method Solve by balancing the equation Subtract from both sides. Multiply both sides by, which is the reciprocal of the coefficient. Reteach Course A 93
3 Method Solve by multiplying the equation by the least common denominator (LCD). 0 0 Multiply both sides by 0, the LCD of and Subtract from both sides. Divide both sides by gives the solution of the equation. Check: Substitute 4 4 for x into the original equation. 3 When 4, the equation is true. gives the solution Method Solve by balancing the equation x 94 Chapter 4 Lesson 4. Subtract from both sides. Multiply both sides by.
4 Method Solve by multiplying the equation by the least common denominator (LCD) Multiply both sides by LCD. Subtract from both sides. Divide both sides by. gives the solution of the equation 3 6. Check: Substitute for x into the original equation When, the equation 3 6 is. gives the solution w 3 4 Reteach Course A 9
5 Solve the equation with variables on the same side Group like terms Add.3 to both sides Divide both sides by.3. 3 Complete Group like terms Add to both sides. Divide both sides by. Solve each equation with variables on the same side y 0.6y.4 96 Chapter 4 Lesson 4.
6 3 4 Method Isolate the variable on the left side of the equation x Subtract x from both sides Subtract 3 to both sides x Divide both sides by Method Isolate the variable on the right side of the equation x Add 4x to both sides. 3 6x 3 6 Subtract from both sides. 8 6x x x Divide both sides by 6. Remember to check your solution by substituting 4 for x into the original 3 equation Subtract x from both sides Subtract 0 from both sides. 6 Divide both sides by. Reteach Course A 97
7 y 4 3y Isolate the variable on the left side x Subtract 0.9x from both sides Add. to both sides x.6 Divide both sides by y..3y p.p 4. 4.m 0.6.8m 98 Chapter 4 Lesson 4.
8 3 m m Method Solve by balancing the equation. 6 m m 6 m m 3 4 m 3 4 m Subtract m 3 9 m m 3 m m 6 m 6 m 0 m from both sides. The LCD of and 3 is. 0 m m; m 9 m. Group like terms. Add to both sides. 3 Method Solve by multiplying both sides of the equation by the LCD. 6 m m Multiply both sides by the reciprocal of,. 6 m m Multiply both sides by, the LCD of 6, 3, 3 4, and. 6 m m 0m 4 9m 6 0m 4 9m 9m 6 9m m 4 6 m m 0 Subtract 9m from both sides. Add 4 to both sides. Remember to check your solution by substituting 0 for m into the original equation. Reteach Course A 99
9 6. 3 y y 7 4 y 3 y 7 4 Subtract 3 y from both sides. 4 The LCD of 7 and 3 4 is 4. 7 y. Group like terms. y Subtract from both sides. ( y) ( ) y Multiply both sides by 7. 3 x x Multiply both sides by the LCD, Subtract x from both sides. 8 3 x p p x x 3 4 y y Subtract from both sides. Divide both sides by. 00 Chapter 4 Lesson 4.
10 ( ) Method Use the distributive property to expand the expression. ( ) 8 8 Method Use inverse operations. ( ) ( ) Subtract from both sides. Multiply both sides by. Express in simplest form. Multiply both sides by. Subtract from both sides. 0. (y 6) 3 3 (y 6) 3 3 (y 6) 3 Multiply both sides by. 3 y 9 y 6 9 Subtract 6 from both sides. y Divide both sides by. y Reteach Course A 0
11 . (3 4) 7. (m 4).4.(n ) 6.4. n. 6.n n n..n... n Subtract 4.8 from both sides. Divide both sides by (6 x) 30 4(6 x) Group like terms. 30 Subtract from both sides. 4. y 3(y ) Divide both sides by. 3(p ) p 4. 0 Chapter 4 Lesson 4.
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