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Questions and Answers
Solving the equation $2(x - 2) = 8$ results in $x = 8$.
Solving the equation $2(x - 2) = 8$ results in $x = 8$.
False
In the equation $7(x + 4) = 2(5x - 4)$, if solved correctly, the solution will yield $x = 6$.
In the equation $7(x + 4) = 2(5x - 4)$, if solved correctly, the solution will yield $x = 6$.
True
The solution to the equation $-99x = 33$ is $x = - rac{1}{3}$.
The solution to the equation $-99x = 33$ is $x = - rac{1}{3}$.
False
In the equation $32/5 x + 16x/5 + 4/5 = 10$, the value of $x$ when solved is $x = 2$.
In the equation $32/5 x + 16x/5 + 4/5 = 10$, the value of $x$ when solved is $x = 2$.
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The equation $4(x - 3) = 4(3x + 1)$ simplifies to $x = - rac{3}{5}$.
The equation $4(x - 3) = 4(3x + 1)$ simplifies to $x = - rac{3}{5}$.
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Study Notes
Solving Linear Equations
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Method 1: Balancing Method
- Solve for 'x' by performing the same operation on both sides of the equation to isolate 'x'.
- Important: Operations include addition, subtraction, multiplication, or division.
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Method 2: Transposition Method
- Isolate the variable term on one side of the equation by moving the constant terms to the opposite side.
- Change the signs of the terms during transposition.
- This helps in solving equations step-by-step.
Example Problems (Using Balancing Method)
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Problem a) 32x + 8x + 2 = -10
- Combining like terms: 40x + 2 = -10
- Subtract 2 from both sides: 40x = -12
- Divide both sides by 40: x = -12/40 which simplifies to x = -3/10
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Problem d) 32x + 16x/4 = 10
- Simplify fraction: 32x + 4x = 10
- Combine like terms: 36x = 10
- Divide both sides by 36: x = 10/36 which simplifies to x = 5/18
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Problem g) 0.34x + 2.4 = 6.5x
- Isolate x terms on one side by subtracing 0.34x from both sides: 2.4 = 6.16x
- Divide by 6.16 on both sides: x = 24/616 = 0.39
Example Problems (Using Transposition Method)
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Problem j) 7 + 4(3x-1) = 2x - 3
- Distribute the 4: 7 + 12x - 4 = 2x - 3
- Combine like terms: 3 + 12x = 2x - 3
- Subtract 2x from both sides: 3 + 10x = -3
- Subtract 3 from both sides: 10x = -6
- Divide both sides by 10: x = -6/10 which simplifies to x = -3/5
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Problem k) 7x - 5x - 0.3 = 2.1/6
- Combine like terms: 2x - 0.3 = 0.35
- Add 0.3 to both sides: 2x = 0.65
- Divide both sides by 2: x = 0.325
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Problem c) 2(x-2) = 8
- Distribute the 2: 2x - 4 = 8
- Add 4 to both sides: 2x = 12
- Divide both sides by 2: x = 6
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Problem e) 2 - 11x = 5x - 4
- Add 11x to both sides: 2 = 16x - 4
- Add 4 to both sides: 6 = 16x
- Divide both sides by 16: x = 6/16 = 3/8
Verification steps
- Substitute the calculated value of 'x' back into the original equation.
- Simplify both sides and if the equation holds true, verified your solution.
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Description
This quiz focuses on solving linear equations using balancing and transposition methods. You will learn to isolate the variable 'x' and apply step-by-step techniques to solve various equation problems. Practicing these methods will strengthen your algebra skills.
