Solve Linear Equations and Rewrite Formulas

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Lesson 1-3
Solve Linear Equations and Rewrite Formulas
At the end of this lesson you will be able to
solve linear equations and rewrite formulas.
Key Vocabulary Equation Linear
Equation Solution Equivalent Equations Formula
Solve for a variable

• -Statement that 2 expressions
• are equal
• Equation that can be written in the
• form ax b 0
• -A number that substitutes for the variable and
  makes a true statement
• Two equations with the same solution
• An equation that relates two or more quantities
• To rewrite an equation as an equivalent equation
  for one variable in terms of the other variables.

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EXAMPLE 1
Solve an equation with a variable on one side
Write original equation.
Subtract 8 from each side.
x 15
Simplify.
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EXAMPLE 2
Write and use a linear equation
During one shift, a waiter earns wages of 30 and
gets an additional 15 in tips on customers food
bills. The waiter earns 105. What is the total
of the customers food bills?
SOLUTION
105 30 0.15x
Write equation.
75 0.15x
Subtract 30 from each side.
500 x
Divide each side by 0.15.
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for Examples 1 and 2
GUIDED PRACTICE
Solve the equation. Check your solution.
1. 4x 9 21
2. 7x 41 13
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EXAMPLE 3
Standardized Test Practice
SOLUTION
7p 13 9p 5
Write original equation.
13 2p 5
Subtract 7p from each side.
18 2p
Add 5 to each side.
9 p
Divide each side by 2.
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EXAMPLE 4
Solve an equation using the distributive property
Solve 3(5x 8) 2(x 7) 12x.
3(5x 8) 2(x 7) 12x
Write original equation.
15x 24 2x 14 12x
Distributive property
15x 24 10x 14
Combine like terms.
25x 24 14
Add 10x to each side.
25x 10
Add 24 to each side.
Divide each side by 25 and simplify.
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for Examples 3 and 4
GUIDED PRACTICE
Solve the equation. Check your solution.
4. 2x 9 2x 7
5. 10 x 6x 15
6. 3(x 2) 5(x 4)
7. 4(2x 5) 2(x 9) 4x
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EXAMPLE 5
Rewrite a formula with two variables
Solve the formula C 2pr for r. Then find the
radius of a circle with a circumference of 44
inches.
SOLUTION
C 2pr
Write circumference formula.
Divide each side by 2p.
Substitute 44 for C and simplify.
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for Example 5
GUIDED PRACTICE
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EXAMPLE 6
Rewrite a formula with three variables
SOLUTION
P 2l 2w
Write perimeter formula.
P 2l 2w
Subtract 2l from each side.
Divide each side by 2.
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EXAMPLE 6
Rewrite a formula with three variables
Substitute 41 for P and 12 for l.
w 8.5
Simplify.
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for Example 6
GUIDED PRACTICE