SUMMARY: The chapter "Simple Equations" introduces students to the concept of equations and how to solve them. KEY TOPICS: introduction to equations, solving equations, transposing terms, applications of simple equations, verifying solutions, forming equations, understanding equality, balancing method, practical problems, word problems.
What is the first step in solving the equation 2x + 5 = 15?
ASubtract 5 from both sides
BAdd 5 to both sides
CMultiply both sides by 2
DDivide both sides by 2
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Correct answer: Option 1 — Subtract 5 from both sides
Q21 Mark
If 3x - 7 = 11, what is the value of x?
A6
B5
C4
D3
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Correct answer: Option 2 — 5
Q31 Mark
Which of the following represents the equation for 'twice a number decreased by 4 equals 10'?
A2x - 4 = 10
B2x + 4 = 10
Cx/2 - 4 = 10
D2x + 4 = 20
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Correct answer: Option 1 — 2x - 4 = 10
Q41 Mark
In the equation 5(x - 2) = 15, what is the first step to solve for x?
AAdd 2 to both sides
BDivide both sides by 5
CSubtract 15 from both sides
DDistribute the 5
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Correct answer: Option 4 — Distribute the 5
Q51 Mark
Which of the following statements is true about the equation x + 3 = 10?
Ax = 7 is a solution
Bx = 6 is a solution
Cx = 10 is a solution
Dx = 3 is a solution
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Correct answer: Option 1 — x = 7 is a solution
Short Answer Questions5 questions
Q63 Marks
What is an equation and how does it differ from an expression?
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An equation is a mathematical statement that asserts the equality of two expressions, typically involving variables. Unlike an expression, which represents a value, an equation shows a relationship that can be solved for unknown values.
Q73 Marks
Explain the process of transposing terms in an equation. Give an example.
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Transposing terms involves moving a term from one side of the equation to the other, changing its sign in the process. For example, in the equation x + 5 = 12, if we transpose 5 to the other side, we get x = 12 - 5, which simplifies to x = 7.
Q83 Marks
How do you verify the solution of a simple equation?
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To verify the solution of a simple equation, substitute the value of the variable back into the original equation. If both sides of the equation are equal after substitution, the solution is verified as correct.
Q93 Marks
Form an equation based on the statement: 'Three times a number decreased by 4 is equal to 11.'
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Let the unknown number be represented by x. The equation formed from the statement is 3x - 4 = 11.
Q103 Marks
Solve the equation 2x + 3 = 15 and explain each step.
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To solve 2x + 3 = 15, first subtract 3 from both sides to get 2x = 12. Then, divide both sides by 2 to find x = 6. Each step maintains the equality of the equation.
Long Answer Questions5 questions
Q116 Marks
Explain the process of solving a simple equation using the balancing method. Provide an example to illustrate your explanation.
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The balancing method involves performing the same operation on both sides of an equation to maintain equality. To solve a simple equation, you first isolate the variable on one side. For example, consider the equation 2x + 3 = 11. To solve for x, subtract 3 from both sides, resulting in 2x = 8. Next, divide both sides by 2 to isolate x, yielding x = 4. This method ensures that the equation remains balanced throughout the solution process.
Q126 Marks
A number is added to 15, and the result is 30. Formulate the equation and solve for the unknown number. Explain each step.
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Let the unknown number be represented by x. The situation can be expressed as the equation x + 15 = 30. To solve for x, we first isolate the variable by subtracting 15 from both sides, leading to x = 30 - 15. Simplifying this gives x = 15. Thus, the unknown number is 15. Each step involves maintaining the equality of the equation while isolating the variable.
Q136 Marks
Describe how to verify the solution of an equation. Use the equation 3x - 4 = 5 as an example and demonstrate the verification process.
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To verify the solution of an equation, substitute the value of the variable back into the original equation to check if both sides are equal. For the equation 3x - 4 = 5, let's solve for x first. Adding 4 to both sides gives 3x = 9, and dividing by 3 results in x = 3. To verify, substitute x = 3 back into the original equation: 3(3) - 4 = 5, which simplifies to 9 - 4 = 5. Since both sides are equal, the solution is verified.
Q146 Marks
Discuss the concept of transposing terms in an equation. Provide an example where you transpose terms to solve for a variable.
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Transposing terms involves moving a term from one side of the equation to the other while changing its sign. This is a crucial step in solving equations. For example, consider the equation x + 7 = 12. To solve for x, we can transpose 7 to the right side, changing its sign to negative: x = 12 - 7. This simplifies to x = 5. Transposing helps in isolating the variable and is essential for maintaining the equation's balance.
Q156 Marks
Create a word problem that can be modeled by a simple equation, solve it, and explain the steps taken to arrive at the solution.
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A word problem could be: 'A shopkeeper has some apples. After selling 20 apples, he has 50 left. How many apples did he start with?' Let the initial number of apples be x. The equation can be formed as x - 20 = 50. To solve for x, we add 20 to both sides, resulting in x = 50 + 20, which simplifies to x = 70. Thus, the shopkeeper started with 70 apples. The steps include forming the equation based on the problem statement and then solving it by isolating the variable.
Assertion–Reason Questions5 questions
Q161 Mark
Assertion (A): An equation is a mathematical statement that asserts the equality of two expressions.
Reason (R): The equality sign '=' indicates that the values on both sides are the same.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q171 Mark
Assertion (A): To solve the equation 2x + 3 = 11, we can subtract 3 from both sides.
Reason (R): This is an example of transposing terms to isolate the variable.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q181 Mark
Assertion (A): If x = 5 is a solution to the equation 3x - 7 = 8, then substituting x back into the equation will yield a true statement.
Reason (R): Verifying solutions is not necessary after finding them.
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Correct answer: Option 3 —
A is true, but R is false.
Q191 Mark
Assertion (A): The equation 4y + 2 = 10 can be solved by dividing both sides by 2.
Reason (R): Dividing both sides of an equation maintains the equality.
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Correct answer: Option 4 —
A is false, but R is true.
Q201 Mark
Assertion (A): In a word problem, forming an equation is the first step to finding the solution.
Reason (R): Understanding the problem is more important than forming the equation.
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Correct answer: Option 3 —
A is true, but R is false.
Statement-Based Questions5 questions
Q211 Mark
Statement 1: An equation is a mathematical statement that asserts the equality of two expressions.
Statement 2: To solve an equation, we can change the order of operations without affecting the equality.
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Correct answer: Option 1 —
Both statements are true.
Q221 Mark
Statement 1: Transposing terms involves moving a term from one side of the equation to the other while changing its sign.
Statement 2: The solution of an equation is the value that makes the equation false.
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Correct answer: Option 3 —
Only Statement 2 is true.
Q231 Mark
Statement 1: Verifying a solution means substituting the solution back into the original equation to check if both sides are equal.
Statement 2: The balancing method requires us to perform the same operation on both sides of the equation to maintain equality.
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Correct answer: Option 1 —
Both statements are true.
Q241 Mark
Statement 1: In word problems, forming an equation is unnecessary if the problem can be solved using arithmetic operations only.
Statement 2: Simple equations can be applied to solve real-life problems, such as calculating age or distance.
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Correct answer: Option 2 —
Only Statement 1 is true.
Q251 Mark
Statement 1: Understanding equality means recognizing that both sides of an equation must have the same value.
Statement 2: An equation can have multiple solutions that satisfy it simultaneously.
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Correct answer: Option 2 —
Only Statement 1 is true.
