Algebraic Equation

Q.

Each student in a class of $40$, studies at least one of the subjects English, Mathematics and Economics. $16$ study English, $22$ Economics and $26$ Mathematics, $5$ study English and Economics, $14$ Mathematics and Economics and $2$ study all the three subjects. The number of students who study English and Mathematics but not Economics is

1. $7$

2. $5$

3. $10$

4. $4$

Q.

Variables of the objective function of the linear programming problem are

1. zero

2. zero or positive

3. negative

4. zero or negative

Q. When a number x is multiplied by itself n number of times, we represent the product as $x^n$. The value n is known as the _____ of x

1. Power
2. Exponent
3. Coefficient
4. Expression

Q. The highest exponent of any variable in a linear expression is

1. 0
2. 1
3. 2
4. 13

Q.

Write an equation for the given statement: A number multiplied by itself is $12$ more than the number.

Q. In a parade of $n$ rows of soldiers, there are 10 soldiers in each row. Total number of soldiers in the parade rises to $50$ after one more row is added. For the given problem, which of the following algebraic equation holds true?

1. $10n=50$
2. $10n+10=50$
3. $10n-10=50$
4. None of the above

Q. If LHS is not equal to RHS then it's not an equation.

1. False
2. True

Q.

An equation is a mathematical statement that shows that two ___ are equal.

1. expressions

2. variables

3. Logical values

4. symbols

Q. Which among the following is an equation?

1. x+y>4
2. x+y<4
3. x+y
4. x+y=4

Q.

Express as an equation:

$5$ less than five times a number is $35$.

Q.

Express s an equation:

Four times of a number subtracted from $24$ is $8$.

Q. A class has ${}^{\prime }{N}^{\prime }$ number of students. For a project, Ms. Smith divides students into 6 groups such that each group consists of 8 students. Find the equation that captures this situation.

1. $\frac{N}{8}=6$
2. $\frac{N}{6}=8$
3. $N-6=8$

Q. A hen laid some eggs. After a few days, 16 eggs were hatched. There were 9 more eggs yet to be hatched. What is the equation that represents the total number of eggs the hen laid?

1. $x+16=9$
2. $x-9=16$
3. $x-16=9$

Q.

You can spend no more than $\$100$ on a party you are hosting. The cost per guest is $\$8$.
(A). Write and solve an inequality that represents the numbers of guests you can invite to the party.
(B). What is the greatest number of guests that you can invite to the party? Explain your reasoning.

Q.

The three equations given below are exactly same equations.

1. True
2. False

Q. The algebraic equation $3x+27=7$ can be written as $3x=7+27$.

1. True
2. False

Q.

Write an equation for the following:

If one-tenth of a number $x$ is subtracted from seven times the number, then the result is $138$.

Q. Express the following as an algebraic expression:
Subtract $3a$ from $n$ and then add $3b$ to it.

1. $n-3a-3b$
2. $n+3a+3b$
3. $n+3a-3b$
4. $n-3a+3b$

Q. The process of determining the value of the unknown from an algebraic expression is called solving the equations for the unknown.

1. True
2. False

Q. If LHS is not equal to RHS then it's not an equation.

1. False
2. True

Q. In the algebraic expression 'p + 5', is a variable.

1. p
2. +
3. 5

Q. What do we get when we convert the statement : "3 added to 2 times x is 10" to an algebraic equation?

1. $2x=10$
2. $2x+3=10$
3. $3x+2=10$
4. $x+3=10$

Q. Whenever change we make to an equation, is made on both sides of the equation.

1. True
2. False

Q. Which of the following is a linear (or simple) equation in one variable? Give reasons. [4 MARKS]

(i) $x^2=5$

(ii) $x+y=4$

(iii) $x+6=9$

(iv) $x^2+y^2=9$

Q. A spaceship landed near Alex's house. Alex saw that the aliens who walked out had 3 legs each. He counted a total of 24 legs. If ${}^{\prime }{x}^{\prime }$ is the number of aliens, find the equation for the number of legs of the aliens.

1. $3x=24$
2. $24x=3$
3. $x+3=24$

Q. Which of the following expressions gives the equivalent expression of 3(2x - 7y - 3)?

1. 6x - 21y - 9
2. 6x + 14y + 9
3. 3x - 14y - 9
4. 6x - 7y - 9

Q. Statement 1: x + 2
Statement 2: x + 2 = 8
Which of the option is correct regarding statement 1 and statement 2?

1. Statement 1 is an algebraic expression
2. Statement 1 is an algebraic equation
3. Statement 2 is an algebraic expression
4. Statement 2 is an algebraic equation

Q. What is the algebraic expression the quotient of a number and $8$?

Q. $7\times 3-1=22$

1. True
2. False

Q.

State which of the following is an algebraic equation.

1. 7 = (11 × 5) - (12 × 4)

2. (7 × 3) - 19 = 8

3. 2m < 30

4. 20 = 5y