algebra 1 lesson 2-2 warm-up. algebra 1 lesson 2-2 warm-up

ALGEBRA 1

Lesson 2-2 Warm-Up

ALGEBRA 1

“Solving Multi-Step Equations” (2-2)

What are the steps for solving a multi-step equation?

Step 1: Clear the equation of fractions and decimals. You can clear decimals by using the decimal that has the most digits after it and moving all of the decimals that number of jumps to the right.

Example: 0.5a2 + 0.875 = 13.25

Since 0.875 is the greatest number of place values from the end (3), jump all of the decimals 3 places to the right, so 0.5a2 + 0.875 = 13.25 is the same as 500a2 + 875 = 13,250

Step 2: Use the Distributive Property to remove parenthesis if you can’t simplify the problem within them.

Step 3: Combine like terms on each side.

Step 4: “Undo” (since you’re working backwards) addition and subtraction.

Step 5: Undo multiplication and division.

ALGEBRA 1

Solve 3a + 6 + a = 90

4a + 6 = 90 Combine like terms.4a + 6 = 90 Subtract 6 from each side.

-6 - 6 4a =84 Simplify.

3a + 6 + a = 90Check:

90 = 90

63 + 6 + 21 90

3(21) + 6 + 21 90 Substitute 21 for a.

a = 21 Simplify.

= Divide each side by 4. 4a4

844

Solving Multi-Step EquationsLESSON 2-2

Additional Examples

ALGEBRA 1

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 width of x ft and the length will be 25 ft.

What is the greatest width the pen can be if you have 63 ft of

fencing?

Words: width plus 25 ft plus width equals amount of side of side of fencing

Define: Let x = width of a side

Equation: x + 25 + x = 63


Additional Examples

ALGEBRA 1

x + 25 + x = 63

The pen can be 19 ft long.

2x + 25 = 63 Combine like terms (1x + 1x = 2x).

2x + 25 = 63 Subtract 25 from each side.

- 25 - 25

2x = 38 Simplify.

x = 19

(continued)

= Divide each side by 2. 2x2

382


Additional Examples

ALGEBRA 1

Solve 2(x – 3) = 8

2x – 6 = 8 Use the Distributive Property.2x – 6 = 8 Add 6 to each side.

+ 6 + 6 2x = 14 Simplify.

x = 7 Simplify.

= Divide each side by 2. 2x2

142


Additional Examples

ALGEBRA 1

Solve + = 173x2

x5

x = 10 Simplify.

Method 1: Finding common denominators

+ = 173x2

x5

x + x = 17 Rewrite the equation.32

15

x = 17 Combine like terms. 1710

( x) = (17) Multiply each side by the reciprocal of , which is .

1710

1017

1017 17

101017

x + x = 17 A common denominator of and is 10. 1510

210

32

15


Additional Examples

ALGEBRA 1

15x + 2x = 170 Multiply.

17x = 170 Combine like terms.

x = 10 Simplify.

Method 2: Multiplying to clear fractions

+ = 173x2

x5

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

(continued)


Additional Examples

ALGEBRA 1

Solve 0.6a + 18.65 = 22.85.

100(0.6a + 18.65) = 100(22.85) The greatest number of decimal

places is two places, so multiply

each side by 102 or 100.

100(0.6a) + 100(18.65) = 100(22.85) Use the Distributive Property.60a + 1865

= 2285 Simplify. 60a + 1865 = 2285

Subtract 1865 from each side.

- 1865 - 1865 60a =420

Simplify.

a =7 Simplify.

= Divide each side by 60.

60a60

42060


Additional Examples

ALGEBRA 1

Solve each equation.

1. 4a + 3 – a = 24 2. –3(x – 5) = 66

3. + = 7 4. 0.05x + 24.65 = 27.5n3

n4

7 –17

12 57


Lesson Quiz

algebra 1 lesson 2-2 warm-up. algebra 1 lesson 2-2 warm-up

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