Transcript Solve Multi-step equations

Use with Lesson 5
MAFS.8.EE.3.7
Solve each equation. Check your solution.
1. 8b – 12 = 5b
2. 5c + 24 = c
3. 3x + 2 = 2x – 3
4. 4n – 3 = 2n + 7
5. Todd is trying to decide between two jobs. Job A
pays $400 per week plus a 20% commission on
everything sold. Job B pays $500 per week plus a
15% commission on everything sold. How much
would Todd have to sell each week for both jobs to
pay the same? Write an equation and solve.
Course 3, Lesson 2-5
Mathematics Florida Standards – Mathematics, numbering and wording from www.cpalms.org.
Use with Lesson 5
MAFS.8.EE.3.7
ANSWERS
1. 4
2. −6
3. −5
4. 5
5. 400 + 0.20x = 500 + 0.15x; $2,000
Course 3, Lesson 2-5
Mathematics Florida Standards – Mathematics, numbering and wording from www.cpalms.org.
WHAT is equivalence?
Course 3, Lesson 2-5
• MAFS.8.EE.3.7
Solve linear equations in one variable.
• MAFS.8.EE.3.7a
Give examples of linear equations in one variable with one solution,
infinitely many solutions, or no solutions. Show which of these
possibilities is the case by successively transforming the given equation
into simpler forms, until an equivalent equation of the form x = a, a = a, or
a = b results (where a and b are different numbers).
• MAFS.8.EE.3.7b
Solve linear equations with rational number coefficients, including
equations whose solutions require expanding expressions using the
distributive property and collecting like terms.
Course 3, Lesson 2-5
Mathematics Florida Standards – Mathematics, numbering and wording from www.cpalms.org.
Mathematical Practices
MP1 Make sense of problems and persevere in solving them.
MP2 Reason abstractly and quantitatively.
MP3 Construct viable arguments and critique the reasoning of others.
MP4 Model with mathematics.
Course 3, Lesson 2-5
Mathematics Florida Standards – Mathematics, numbering and wording from www.cpalms.org.
To solve
• multi-step equations,
• equations with no solutions,
• equations with an infinite number of
solutions
Course 3, Lesson 2-5
Symbols
• null set
• empty set
• identity
Course 3, Lesson 2-5
Ø
{}
Null Set
One Solution
Identity
Words
no solution
one solution
infinitely many solutions
Symbols
a=b
x=a
a=a
Example
3x + 4 = 3x
4=0
Since 4 ≠ 0,
there is no
solution.
2x = 20
x = 10
4x + 2 = 4x + 2
2=2
Since 2 = 2, the
solution is all
numbers.
Course 3, Lesson 2-5
WHAT is equivalence?
Course 3, Lesson 2-5
WHAT is equivalence?
Sample answers:
• When the expressions on each side of the equals sign
are the same, the equation is an identity and the
solution is all real numbers.
• When the final step in solving an equation produces
expressions that are not the same, the solution to the
equation is the null set.
Course 3, Lesson 2-5
Describe how the previous
lesson on solving equations
with variables on each side
helped you with today’s
lesson on solving multi-step
equations.
Course 3, Lesson 2-5