Download Solving Equations

Solving Equations
Friday Aug 28
2-3 and 2-4
Rewind
Work problems at your whiteboard.
*Find the calculator with your number
and put it on your desk.
Solve for the variable
1.) x – 11 = 15
2.) -56 = 7y
3.) x + 5 = 28
4.) 2(x + 3) = 14
Why?
• https://www.youtube.com/watch?v=qVsxk_XMLzo
• The Tour de France is the premier cycling event in
the world. If the length of the shortest portion of
the race can be represented by k, the expression
6k + 50.5 is the length of the longest stage or
242.5km. Write an equation that represents the
longest stage of the race.
TEKS
Targeted TEKS
A.5(A) Solve linear equations in one variable,
including those for which the application of the
distributive property is necessary and for which
variables are included on both sides.
Mathematical Processes
A.1(E), A.1(F)
You solved multi-step equations.
• Solve equations with the variable on each
side.
• Solve equations involving grouping symbols.
Solve Multi-Step Equations
A. Solve 2q + 11 = 3. Check your solution.
2q + 11 = 3
2q + 11 – 11 = 3 – 11
2q = –8
Original equation
Subtract 11 from each side.
Simplify.
Divide each side by 2.
q = –4
Simplify.
Answer: q = –4
To check, substitute –4 for q in the original equation.
A. Solve 6v + 7 = –5. Check your solution.
A. v = –2
B. v = –6
C. v = 2
D.
Solve an Equation with Grouping Symbols
Example 2
Original equation
6 + 4q = 12q – 42
Distributive Property
6 + 4q – 12q = 12q – 42 – 12q Subtract 12q from each
side.
6 – 8q = –42
6 – 8q – 6 = –42 – 6
–8q = –48
Simplify.
Subtract 6 from each
side.
Simplify.
Solving Steps
1.) Distribute
2.) Combine Like Terms
3.) Add/Subtract
4.) Multiply/Divide
5.) Check your answer
Board Practice Instructions
• Please pick 3 problems to do.
• Solve for the variable AND check your answer by
substitution (plugging in)
• When the teacher checks an answer, give yourself a
check and erase that problem
• When finished with 3 problems, assist your neighbor
Board practice
Tier 1
Tier 2
1.) 2x + 7 = 3x
5.) 3(x + 1) = 18
2.) 4x = 5 + 5x
6.) 2x – 5x + 2 = -9x – 6
3.) 6x + 2 = -5x
7.) 4x = -2(x + 3)
4.) 10x = 9x + 1
8.) 5(2x – 4) = 40
• 2(x + 6) = 2x + 12
Types of Solutions
• One Solution
• No solution: variable cancels and you get
something untrue (0 = 5)
• All real numbers: variable cancels and you get
something always true (4 = 4)
Tour de France ctd
1.) Solve 6k + 50.5 = 242.5.
2.) What does your answer represent?
Quiz