Les 2 3 Solving Equations by Multiplication Division

Les. 2 -3 – Solving Equations by Multiplication & Division Learning Goal Solve one-step equations in one variable by using multiplication or division

Solving an equation that contains multiplication or division is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable. Inverse Operations Operation Multiplication Division Inverse Operation Division Multiplication

Solving Equations by Using Multiplication Solve the equation. j – 8 = 3 Since j is divided by 3, multiply both sides by 3 to undo the division. – 24 = j Check j – 8 = 3 – 8 – 24 3 – 8 To check your solution, substitute – 24 for j in the original equation.

Solving Equations by Using Multiplication Solve the equation. n = 2. 8 6 Since n is divided by 6, multiply both sides by 6 to undo the division. n = 16. 8 n = 2. 8 Check 6 To check your solution, 16. 8 2. 8 substitute 16. 8 for n in the 6 2. 8 original equation.

Try This! Solve the equation. Check your answer. p = 10 5 Since p is divided by 5, multiply both sides by 5 to undo the division. p = 50 Check p = 10 5 To check your solution, 50 10 substitute 50 for p in the 5 10 10 original equation.

Try This! Solve the equation. Check your answer. y – 13 = 3 Since y is divided by 3, multiply both sides by 3 to undo the division. – 39 = y y Check – 13 = 3 To check your solution, – 39 – 13 substitute – 39 for y in the 3 – 13 original equation.

Solving Equations by Using Division Solve the equation. Check your answer. 9 y = 108 y = 12 Check Since y is multiplied by 9, divide both sides by 9 to undo the multiplication. 9 y = 108 9(12) 108 To check your solution, substitute 12 for y in the 108 original equation.

Solving Equations by Using Division Solve the equation. Check your answer. – 4. 8 = – 6 v 0. 8 = v Since v is multiplied by – 6, divide both sides by – 6 to undo the multiplication. Check – 4. 8 = – 6 v – 4. 8 – 6(0. 8) – 4. 8 To check your solution, substitute 0. 8 for v in the original equation.

Try This! Solve the equation. Check your answer. 16 = 4 c 4=c Check Since c is multiplied by 4, divide both sides by 4 to undo the multiplication. 16 = 4 c 16 16 4(4) 16 To check your solution, substitute 4 for c in the original equation.

Try This! Solve the equation. Check your answer. 15 k = 75 k=5 Since k is multiplied by 15, divide both sides by 15 to undo the multiplication. Check 15 k = 75 15(5) 75 To check your solution, 75 substitute 5 for k in the 75 original equation.

Remember that dividing is the same as multiplying by the reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.

Solving Equations That Contain Fractions Solve the equation. 5 w = 20 6 The reciprocal of 5 is 6. Since w is 6 5 5 multiplied by , multiply both sides 6 6 by. 5 w = 24 Check 5 w = 20 6 20 20 20 To check your solution, substitute 24 for w in the original equation.

Solving Equations That Contain Fractions Solve the equation. 3 = 1 z 16 8 The reciprocal of 1 is 8. Since z is 8 1 multiplied by , multiply both sides 8 by 8. 3=z 2 3 =1 z Check 16 8 To check your solution, substitute 3 for z in the 2 original equation. 3 3 16 16

Try This! Solve the equation. Check your answer. 1 – 1 = b 5 4 5=b – 4 Check – The reciprocal of 1 is 5. Since b is 5 1 multiplied by , multiply both sides 5 by 5. 1 =1 b 4 5 To check your solution, substitute – 5 for b in the 4 original equation.

Properties of Equality WORDS NUMBERS ALGEBRA Addition Property of Equality You can add the same number to both sides of an equation, and the statement will still be true. 3=3 3+2=3+2 5=5 a=b a+c=b+c

Properties of Equality WORDS NUMBERS ALGEBRA Subtraction Property of Equality You can subtract the same number from both sides of an equation, and the statement will still be true. 7=7 7– 5=7– 5 2=2 a=b a–c=b–c

Properties of Equality WORDS NUMBERS ALGEBRA Multiplication Property of Equality You can multiply both sides of an equation by the same number, and the statement will still be true. 6=6 6(3) = 6(3) 18 = 18 a=b ac = bc

Properties of Equality WORDS Division Property of Equality You can divide both sides of an equation by the same nonzero number, and the statement will still be true. NUMBERS 8 = 8 8 8 = 4 4 2 =2 ALGEBRA a=b (c ≠ 0) a = a c c