2A - Solving linear equations
Solving linear equations containing only one unknown:
To solve a linear equation containing only one unknown term, we use inverse operations to transpose to ‘undo’ the equation to make the unknown the subject.
To solve a linear equation containing only one unknown term, we use inverse operations to transpose to ‘undo’ the equation to make the unknown the subject.
Inverse operations include:
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The order of operations:
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When transposing the equation, we must "undo" it in reverse order to the way the equation "reads".
2A - Example 1: Solving linear equations with only one unknown
Solve each of the following equations for the unknown pronumeral:
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2A - Example 1: Video solution
2A - Example 1: Practice
Question 1: ABC Question 2: ABC 2A - Example 1: Solutions
Question 1: ABC Question 2: ABC |
2A - Example 2: Solving linear equations with only one unknown
Solve each of the following equations for the unknown pronumeral:
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2A - Example 2: Video solution
2A - Example 2: Practice
Question 1: ABC Question 2: ABC 2A - Example 2: Solutions
Question 1: ABC Question 2: ABC |
Solving linear equations containing unknown terms on both sides:
To solve a linear equation containing unknowns on both sides of an equation, we use inverse operations to collect all terms involving the unknown on to only one side of the equation.
To solve a linear equation containing unknowns on both sides of an equation, we use inverse operations to collect all terms involving the unknown on to only one side of the equation.
2A - Example 3: Solving linear equations with unknown terms on both sides
Solve each of the following equations for the unknown pronumeral:
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2A - Example 3: Video solution
2A - Example 3: Practice
Question 1: ABC Question 2: ABC 2A - Example 3: Solutions
Question 1: ABC Question 2: ABC |
Solving linear equations containing brackets:
To solve a linear equation containing brackets, you can either expand the brackets or use an inverse operation to get rid of the term out the front of the brackets.
To solve a linear equation containing brackets, you can either expand the brackets or use an inverse operation to get rid of the term out the front of the brackets.
2A - Example 4: Solving linear equations containing brackets
Solve each of the following equations for the unknown pronumeral:
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2A - Example 4: Video solution
2A - Example 4: Practice
Question 1: ABC Question 2: ABC 2A - Example 4: Solutions
Question 1: ABC Question 2: ABC |
Solving linear literal equations:
To solve a linear literal equation, you will ‘undo’ the equation using inverse operations; however, your answer will involve other pronumerals.
To solve a linear literal equation, you will ‘undo’ the equation using inverse operations; however, your answer will involve other pronumerals.
2A - Example 5: Solving linear literal equations
Solve each of the following literal equations for the pronumeral \(x\):
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2A - Example 5: Video solution
2A - Example 5: Practice
Question 1: ABC Question 2: ABC 2A - Example 5: Solutions
Question 1: ABC Question 2: ABC |
Using CAS to solve linear equations:
Linear, and other, equation can be solved using the solve command on the CAS calculator. To use the command:
Linear, and other, equation can be solved using the solve command on the CAS calculator. To use the command:
Highlight the equation → Interactive → Equation/inequality → Solve
Make sure the variable you are solving for is listed on the screen (to change the variable use the Var keyboard).
2A - Example 6: Solving linear equations (CAS)
Solve each of the following equations for \(x\) using CAS:
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2A - Example 6: Video solution
2A - Example 6: Practice
Question 1: ABC Question 2: ABC 2A - Example 6: Solutions
Question 1: ABC Question 2: ABC |
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Additional Exercises
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Topic Worksheets
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Other Resources
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Solve each of the following equations for the unknown pronumeral
(a) \(2x-18=14\) (b) \(4y+22=0\) Solve the equation \(20-7x=6x-6\) for \(x\).
Solve each of the following equations for the unknown pronumeral
(a) \(3(m-4)+5=6\) (b) \(3-7(x+3)=-4\) |
Solutions:
Question 1: (a) \(x=16\) (b) \(y=-\frac{11}{2}\) Question 2: \(x=2\) Question 3: (a) \(m=\frac{13}{3}\) (b) \(x=-2\) |
Solving linear equations - Worksheet A
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PatrickJMT - Solving linear equations:
PatrickJMT: What does it mean to be a solution?
Decide if each of the following are true or false.
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PatrickJMT: Video tutorial
PatrickJMT: Solution
(a) True (b) False |
Patrickjmt: Solving linear equations
Solve each of the following equations for \(x\):
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Patrickjmt: Video tutorial
PATRICKJMT: Solutions
(a) \(x=2\) (b) \(x=\frac{13}{3}\) (c) \(x=\frac{1}{4}\) (d) \(x=\frac{60}{19}\) |
PatrickJMT: Solving linear equations - Examples
Example 1:
Solve the following equation for \(x\) \[-(-3+x)+4=2(x+3)-6x+7\]Example 2: Solve the following equation for \(x\) \[5-\frac{x}{3}=\frac{4(x+1)}{6}\]Example 3: Solve the following equation for \(x\) \[-(6-(7+x))=10+3(2x-5)\] |
PatrickJMT: Example 1 video
PatrickJMT: Example 2 video
PatrickJMT: Example 3 video
PatrickJMT: Solutions
Example 1: \[x=2\] Example 2: \[x=\frac{13}{3}\] Example 3: \[x=\frac{6}{5}\] |