solving multi-step equations define like terms again: terms with exactly the same variables....
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Solving Multi-Step EquationsSolving Multi-Step Equations
Define like terms again: Terms with exactly the same variables.
Examples:
Define the distributive property again: 6(3x + 2)
Example:
**Steps for Solving a Multi-Step Equation**
Step 1 Clear the equation of fractions and decimals.
Step 2 Use the Distributive Property to remove parentheses on each side.
Step 3 Combine like terms on each side.
Step 4 Undo addition or subtraction.
Step 5 Undo multiplication or division.
Solve 3a + 6 + a = 90
4a + 6 = 90 Combine like terms.
-6 -6 Subtract 6 from each side.
4a = 84 Simplify.
3a + 6 + a = 90Check:
Solving Multi-Step EquationsSolving Multi-Step EquationsALGEBRA 1 LESSON 2-3ALGEBRA 1 LESSON 2-3
2-3
= Divide each side by 4.
a = 21 Simplify.
4a4
844
You try:You try:
3x – 4x + 6 = -23x + (-4x) + 6 = -2 - 1 x + 6 = -2 combined like terms
-6 -6 subtract - 1x = -8 get rid of the negative variable
x = 8
7 = 4m – 2m + 1 7 = 4m + (-2m) + 1 7 = 2m + 1-1 -16 = 2m2 2m = 3
Don’t Forget: CHECK your
solution
Solve 2(x – 6) = 8
2x – 12 = 8 Use the Distributive Property.
+12 +12 Add 6 to each side.
2x = 20 Simplify.
x = 10 Simplify.
Solving Multi-Step EquationsSolving Multi-Step EquationsALGEBRA 1 LESSON 2-3ALGEBRA 1 LESSON 2-3
2-3
= Divide each side by 2. 2x2
202
2x + (-12) = 8
You try:You try:
3 ( k + 8 ) = 21
3k + 24 = 21
- 24 -24
3k = -3
3 3
k = -1
15 = -3(x – 1) + 9
15 = -3x – (-3) + 915 = -3x + 3 + 915 = -3x + 12-12 -123 = -3x-3 -3
-1 = x
You need to build a rectangular pen in your back yard for
your dog. One side of the pen will be against the house. Two sides of
the pen have a length of x ft and the width will be 25 ft. What is the
greatest length the pen can be if you have 63 ft of fencing?
Relate: length plus 25 ft plus length equals amount of side of side of fencing
Define: Let x = length of a side adjacent to the house.
Write: x + 25 + x = 63
Solving Multi-Step EquationsSolving Multi-Step EquationsALGEBRA 1 LESSON 2-3ALGEBRA 1 LESSON 2-3
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x + 25 + x = 63
The pen can be 19 ft long.
2x + 25 = 63 Combine like terms.
– 25 = – 25 Subtract 25 from each side.
2x = 38 Simplify.
x = 19
Solving Multi-Step EquationsSolving Multi-Step EquationsALGEBRA 1 LESSON 2-3ALGEBRA 1 LESSON 2-3
2-3
(continued)
= Divide each side by 2. 2x2
382
Solve + = 173x2
x5
15x + 2x = 170 Multiply.
17x = 170 Combine like terms.
x = 10 Simplify.
Solving Multi-Step EquationsSolving Multi-Step EquationsALGEBRA 1 LESSON 2-3ALGEBRA 1 LESSON 2-3
2-3
Method 2: Multiplying to clear fractions
10( + ) = 10(17) Multiply each side by 10, a commonmultiple of 2 and 5.
3x2
x5
10( ) + 10( ) = 10(17) Use the Distributive Property.3x2
x5
= Divide each side by 17.17x17
17017
You try:You try:
2nd method:
¼ m + ½ m = 5/8
(8) ¼ m + (8) ½ m = 5/8 ( 8)
2m + 4m = 5
6m = 5
6 6
m = 5/6
Solve 0.6a + 18.65 = 22.85.
Solving Multi-Step EquationsSolving Multi-Step EquationsALGEBRA 1 LESSON 2-3ALGEBRA 1 LESSON 2-3
2-3