1. Activating Prior Knowledge – Notes
M4:LSN5
Writing and Solving Linear Equations
Activating Prior Knowledge – Notes
Transcribe the expression using mathematical symbols.
1. Four less than three times a number
2. Six more than half a number
3. Twelve more than three times a number
4. Twice as large as a number
Tie to LO

2. Learning Objective
Today, we will apply knowledge of geometry to writing and solving linear equations.
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3. Concept Development Review
M4:LSN5
Writing and Solving Linear Equations
Concept Development Review
A triangle has three sides and three angles.
The three angles always add up to 180˚.
A right triangle has a 90˚ angle.
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4. Concept Development Review
M4:LSN5
Writing and Solving Linear Equations
Concept Development Review
Congruent means the same size and shape.
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5. Concept Development Review
M4:LSN5
Writing and Solving Linear Equations
Concept Development Review
Complementary and Supplementary Angles.
Angles whose measures add up to 90° are complementary.
Angles whose measures add up to 180° are supplementary.
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6. Concept Development Review – Whiteboard
M4:LSN5
Writing and Solving Linear Equations
Concept Development Review – Whiteboard
Goal – get the variable on one side and the number on the other side of the equation in one move. What is the operation/move?
x - 9 = 10
2.4x = 12
4.5 = -7+x
𝟏 𝟐 +𝒙=−𝟓
𝟖 𝟗 x = 16
CFU

7. Concept Development Review – Whiteboard
M4:LSN5
Writing and Solving Linear Equations
Concept Development Review – Whiteboard
Write down the one operation that could be used to get all of x on one side of the equation in one step.
3x + 6 = 5x
10 - x = 2x
𝟓 𝟗 +𝟒𝒙=𝟖𝒙
𝟐 𝟑 x = 8 + 4x
CFU

8. Skill Development/Guided Practice – Notes #1
M4:LSN4
Solving Linear Equations
Skill Development/Guided Practice – Notes #1
Solve the linear equation 𝒙+𝟑+𝒙−𝟖+𝒙=𝟓𝟓
for the number x.
State the property that justifies your first step and why you chose it.
Check ?
𝒙+𝟑+𝒙−𝟖+𝒙=𝟓𝟓
𝒙+𝟑+𝒙−𝟖+𝒙=𝟓𝟓
𝟑𝒙−𝟓=𝟓𝟓 ?
𝟑𝒙−𝟓=𝟓𝟓
CFU

9. Skill Development/Guided Practice – Notes #2
M4:LSN4
Solving Linear Equations
Skill Development/Guided Practice – Notes #2
Solve the linear equation 𝟏 𝟐 𝒙+𝟏𝟎= 𝟏 𝟒 𝒙+𝟓𝟒
for the number x.
Check
𝟏 𝟐 𝒙+𝟏𝟎= 𝟏 𝟒 𝒙+𝟓𝟒
𝟏 𝟐 𝒙 = 𝟏 𝟒 𝒙+𝟒𝟒 ?
−𝟏𝟎 −𝟏𝟎
𝟏 𝟐 𝒙 = 𝟏 𝟒 𝒙+𝟒𝟒
− 𝟏 𝟒 𝒙 − 𝟏 𝟒 𝒙
𝟏 𝟒 𝒙 =𝟒𝟒
÷ 𝟏 𝟒 ÷ 𝟏 𝟒
𝒙 =𝟏𝟕𝟔
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10. Skill Development/Guided Practice – Notes #3
M4:LSN5
Writing and Solving Linear Equations
Skill Development/Guided Practice – Notes #3
3. The measure of one angle is ten less than four times the measure of the other angle. The sum of the measures of the two angles is 90˚. Determine the measure of each of the angles.
Angle 1:
𝟒𝒙−𝟏𝟎
Angle 2: 𝒙
=𝟐𝟎
𝟒 𝟐𝟎 −𝟏𝟎
=𝟖𝟎−𝟏𝟎
=𝟕𝟎
Check:
Equation:
𝟒𝒙−𝟏𝟎+𝒙=𝟗𝟎
𝟕𝟎+𝟐𝟎=𝟗𝟎
𝟓𝒙−𝟏𝟎=𝟗𝟎
+𝟏𝟎 +𝟏𝟎
𝟗𝟎=𝟗𝟎
𝟓𝒙=𝟏𝟎𝟎
÷𝟓 ÷𝟓
𝒙=𝟐𝟎
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11. Skill Development/Guided Practice – Notes #4
M4:LSN5
Writing and Solving Linear Equations
Skill Development/Guided Practice – Notes #4
4. The angles of a triangle are described as follows: ∠𝐴 𝑖𝑠 𝑡ℎ𝑒
𝑙𝑎𝑟𝑔𝑒𝑠𝑡 𝑎𝑛𝑔𝑙𝑒, 𝑖𝑡𝑠 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑖𝑠 𝑡𝑤𝑖𝑐𝑒 𝑡ℎ𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 ∠𝐵.
𝑇ℎ𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 ∠𝐶 𝑖𝑠 2 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 ℎ𝑎𝑙𝑓 𝑡ℎ𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 ∠𝐵. Find the measures of the three angles.
Angle B:
Angle A: 𝒙
𝟏 𝟐 𝒙−𝟐 𝟐𝒙
=𝟓𝟐
Angle C:
𝟐(𝟓𝟐)
=𝟏𝟎𝟒
𝟏 𝟐 (𝟓𝟐)−𝟐
=𝟐𝟒
Equation:
Check:
𝟐𝒙+𝒙+ 𝟏 𝟐 𝒙−𝟐
=𝟏𝟖𝟎
𝟓𝟐+𝟏𝟎𝟒+𝟐𝟒=𝟏𝟖𝟎
𝟑 𝟏 𝟐 𝒙−𝟐=𝟏𝟖𝟎
𝟏𝟓𝟔+𝟐𝟒=𝟏𝟖𝟎
𝟏𝟖𝟎=𝟏𝟖𝟎
𝟕 𝟐 𝒙=𝟏𝟖𝟐
CFU

12. What does this mean about the two angles?
M4:LSN5
Writing and Solving Linear Equations
Skill Development/Guided Practice – Notes #5
5. A pair of corresponding angles are described as follows: the measure of one angle is five less than seven times a number and the measure of the other angle is eight more than seven times the number. Are the angles congruent? Why or why not?
What does congruent mean?
Angle 2:
Angle 1:
𝟕𝒙+𝟖
𝟕𝒙−𝟓 ?
𝟕𝒙−𝟓=𝟕𝒙+𝟖
−𝟕𝒙 −𝟕𝒙
−𝟓≠𝟖
What does this mean about the two angles?
CFU

13. Independent Practice – Exit Ticket #1
M4:LSN5
Writing and Solving Linear Equations
Independent Practice – Exit Ticket #1
1. Given a right triangle, find the measures of all the angles if one angle is a right angle and the measure of the second angle is six less than seven times the measure of the third angle.
Angle 1:
Angle 2:
Angle 3:
CFU

14. Independent Practice – Exit Ticket #2
M4:LSN5
Writing and Solving Linear Equations
Independent Practice – Exit Ticket #2
2. In a right triangle, find the measures of all the angles if one angle is a right angle and the measure of the second angle is six less than seven times the measure of the third angle.
Angle 1:
Angle 2:
Angle 3:
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15. Closure CFU 1. What did we learn today?
2. Why is this important to you?
3. How can you tell if a value of x is a solution to an equation?
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16. Independent Practice CFU Complete handout – show all work.
*Use separate piece of paper – for work.
CFU