Podcast
Questions and Answers
What is the primary goal when solving an algebraic equation?
What is the primary goal when solving an algebraic equation?
- To simplify the equation by combining like terms.
- To make both sides of the equation equal to zero.
- To isolate the variable on one side of the equation. (correct)
- To eliminate all variables from the equation.
In the equation, $r + 5.2 = 14$, subtracting 5.2 from both sides maintains the equation's balance.
In the equation, $r + 5.2 = 14$, subtracting 5.2 from both sides maintains the equation's balance.
True (A)
What operation is used to undo addition in an algebraic equation?
What operation is used to undo addition in an algebraic equation?
subtraction
In the equation $2n - 3 = 13$, the first step to isolate n is to add 3 to ______ sides of the equation.
In the equation $2n - 3 = 13$, the first step to isolate n is to add 3 to ______ sides of the equation.
Which of the following operations is the inverse of multiplication?
Which of the following operations is the inverse of multiplication?
Dividing both sides of the equation $2(3x + 1) = 14$ by 2 is a valid first step to solve for $x$.
Dividing both sides of the equation $2(3x + 1) = 14$ by 2 is a valid first step to solve for $x$.
In the equation $3x = 6$, what is the value of $x$?
In the equation $3x = 6$, what is the value of $x$?
To solve $4x - 6 = 2x + 2$, the variable terms must be collected on one side of the equation by either adding or ______.
To solve $4x - 6 = 2x + 2$, the variable terms must be collected on one side of the equation by either adding or ______.
When solving $4x - 6 = 2x + 2$, what is the result after subtracting $2x$ from both sides?
When solving $4x - 6 = 2x + 2$, what is the result after subtracting $2x$ from both sides?
The solution to the equation $7b^2 = 343$ is only $b = 7$.
The solution to the equation $7b^2 = 343$ is only $b = 7$.
To solve $b^2 = 49$, what operation is performed on both sides of the equation to find the value of $b$?
To solve $b^2 = 49$, what operation is performed on both sides of the equation to find the value of $b$?
In the equation $4x - 6 = 2x + 2$, the expression 'six less than four times a number' represents ______.
In the equation $4x - 6 = 2x + 2$, the expression 'six less than four times a number' represents ______.
Match each operation with its inverse operation:
Match each operation with its inverse operation:
What is the value of $x$ in the equation $2(3x + 1) = 14$?
What is the value of $x$ in the equation $2(3x + 1) = 14$?
The verification step in solving an equation is optional and does not affect the correctness of the solution.
The verification step in solving an equation is optional and does not affect the correctness of the solution.
What is the solution to the equation $r + 5.2 = 14$?
What is the solution to the equation $r + 5.2 = 14$?
Translating $4x - 6 = 2x + 2$ into words, 'two more than two times the number' refers to the expression ______.
Translating $4x - 6 = 2x + 2$ into words, 'two more than two times the number' refers to the expression ______.
Which operation should be performed first to solve the equation $2n - 3 = 13$?
Which operation should be performed first to solve the equation $2n - 3 = 13$?
In the equation $7b^2 = 343$, the value of $b^2$ is 49.
In the equation $7b^2 = 343$, the value of $b^2$ is 49.
What does 'LS=RS' signify when verifying the solution to an algebraic equation?
What does 'LS=RS' signify when verifying the solution to an algebraic equation?
Flashcards
Algebraic Equation
Algebraic Equation
A mathematical statement showing that two expressions are equal.
Solving Equations
Solving Equations
Isolate the variable by performing the same operations on both sides.
Verifying Solutions
Verifying Solutions
Replace the variable in the original equation with the calculated value.
Solving r + 5.2 = 14
Solving r + 5.2 = 14
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Solving 2n - 3 = 13
Solving 2n - 3 = 13
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Solving 2(3x + 1) = 14
Solving 2(3x + 1) = 14
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Solving 4x - 6 = 2x + 2
Solving 4x - 6 = 2x + 2
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Solving 7b² = 343
Solving 7b² = 343
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Study Notes
- An algebraic equation is a mathematical statement showing the equality of two expressions.
- Example: n + 3 = 5
Solving Equations and Verifying Solutions
- To solve an equation, isolate the variable by performing the same operations on both sides.
- After solving, verify the solution by substituting it back into the original equation.
- The left side (LS) should equal the right side (RS) if the solution is correct.
Example 1a: Solving r + 5.2 = 14
- Subtract 5.2 from both sides: r + 5.2 - 5.2 = 14 - 5.2
- This simplifies to r = 8.8
- Verification: Substitute r = 8.8 into the original equation.
- LS = 8.8 + 5.2 = 14
- RS = 14
- Since LS = RS, r = 8.8 is the correct solution.
Example 1b: Solving 2n - 3 = 13
- Add 3 to both sides: 2n - 3 + 3 = 13 + 3
- This simplifies to 2n = 16
- Divide both sides by 2: 2n / 2 = 16 / 2
- This simplifies to n = 8
- Verification: Substitute n = 8 into the original equation.
- LS = 2(8) - 3 = 16 - 3 = 13
- RS = 13
- Since LS = RS, n = 8 is the correct solution.
Example 1c: Solving 2(3x + 1) = 14
- Divide both sides by 2: 2(3x + 1) / 2 = 14 / 2
- This simplifies to 3x + 1 = 7
- Subtract 1 from both sides: 3x + 1 - 1 = 7 - 1
- This simplifies to 3x = 6
- Divide both sides by 3: 3x / 3 = 6 / 3
- This simplifies to x = 2
- Verification: Substitute x = 2 into the original equation.
- LS = 2(3(2) + 1) = 2(6 + 1) = 2(7) = 14
- RS = 14
- Since LS = RS, x = 2 is the correct solution.
Example 1d: Solving 4x - 6 = 2x + 2
- Add 6 to both sides: 4x - 6 + 6 = 2x + 2 + 6
- This simplifies to 4x = 2x + 8
- Subtract 2x from both sides: 4x - 2x = 2x - 2x + 8
- This simplifies to 2x = 8
- Divide both sides by 2: 2x / 2 = 8 / 2
- This simplifies to x = 4
- Verification: Substitute x = 4 into the original equation.
- LS = 4(4) - 6 = 16 - 6 = 10
- RS = 2(4) + 2 = 8 + 2 = 10
- Since LS = RS, x = 4 is the correct solution.
Example 1e: Solving 7b² = 343
- Divide both sides by 7: 7b² / 7 = 343 / 7
- This simplifies to b² = 49
- Take the square root of both sides: √b² = √49
- This simplifies to b = 7
- Verification: Substitute b = 7 into the original equation.
- LS = 7(7²) = 7(49) = 343
- RS = 343
- Since LS = RS, b = 7 is the correct solution.
Interpreting Equations in Words
- Example: 4x – 6 = 2x + 2 can be interpreted as "Six less than four times a number is equal to two times the same number plus two."
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