Solving Equations with 2 4 Variables on Both
Solving Equations with 2 -4 Variables on Both Sides Objective Solve equations in one variable that contain variable terms on both sides. Holt Algebra 1
Solving Equations with 2 -4 Variables on Both Sides Example 1: Solving Equations with Variables on Both Sides Solve 5 - n – 2 = 6. 3–n=6 – 3 -3 -n = 3 -1 -1 n = -3 Holt Algebra 1 To collect the variable terms on one side, subtract 2 from 5. 3 is hanging on, so subtract 3 from both sides. Since -n is negative, divide both sides by -1.
Solving Equations with 2 -4 Variables on Both Sides Example 1: Solving Equations with Variables on Both Sides Solve 7 n – 2 = 5 n + 6 – 5 n 2 n – 2 = +2 2 n = To collect the variable terms on one side, subtract 5 n from both sides. 6 +2 8 Since n is multiplied by 2, divide both sides by 2 to undo the multiplication. n=4 Holt Algebra 1
Solving Equations with 2 -4 Variables on Both Sides Check It Out! Example 1 a Solve 4 b + 2 = 3 b -3 b – 3 b b+2= 0 – 2 b = – 2 Holt Algebra 1 To collect the variable terms on one side, subtract 3 b from both sides.
Solving Equations with 2 -4 Variables on Both Sides Check It Out! Example 1 b Solve 5 - 3 y = -7 y + 3 + 7 y 5 + 4 y = 3 -5 -5 4 y = -2 4 4 y = -½ Holt Algebra 1 To collect the variable terms on one side, add 4 y to both sides. Since 5 is added to 4 y, subtract 5 from both sides to undo the addition. Since y is multiplied by 4, divide both sides by 4 to undo the multiplication.
Solving Equations with 2 -4 Variables on Both Sides Check It Out! Example 1 b Solve 2 + 4 y = 9 y – 8 – 4 y 2 +8 10 = 5 y – 8 +8 = 5 y 2=y Holt Algebra 1 To collect the variable terms on one side, subtract 4 y from both sides. Since 8 is subtracted from 5 y, add 8 to both sides to undo the subtraction. Since y is multiplied by 5, divide both sides by 5 to undo the multiplication.
Solving Equations with 2 -4 Variables on Both Sides Check It Out! Example 2 b Solve -2 x + 15 + 1 = 2(x + 2)Distribute 2 to the expression in parentheses. -2 x + 15 + 1 = 2(x) + 2(2) -2 x + 15 + 1 = 2 x + 4 -2 x + 16 = 2 x + 4 Combine like terms. To collect the variable terms +2 x on one side, add 2 x to both 16 = 4 x + 4 sides. – 4 Subtract 4 from both sides 12 = 4 x Divide by 4 and simplify. 3=x Holt Algebra 1
Solving Equations with 2 -4 Variables on Both Sides Example 2: Simplifying Each Side Before Solving Equations Solve 12 – 6 a + 4 a = – 1 – 5(7 – 2 a) Distribute – 5 to the expression in parentheses. 12 – 6 a + 4 a = – 1 – 5(7) – 5(– 2 a) 12 – 6 a + 4 a = – 1 – 35 + 10 a 12 – 2 a = – 36 + 10 a + 2 a +2 a 12 +36 48 Holt Algebra 1 = -36 + 12 a +36 = 12 a Combine like terms. To collect the variable terms on one side, add 2 a to both sides. Since – 36 is added to 10 a, add 36 to both sides.
Solving Equations with 2 -4 Variables on Both Sides Example 2 Continued Solve 4 – 6 a + 4 a = – 1 – 5(7 – 2 a). 48 = 12 a 12 12 4=a Holt Algebra 1 Since a is multiplied by 12, divide both sides by 12.
- Slides: 9