Linear Equation in One Variable

Q.

Solve the following equation and check your results: $\frac{2x}{3}+1=\frac{7x}{15}+3$

Q.

Solve $6x+3y=6xy$ and $2x+4y=5xy$$x=1$ by reducing them to pair of linear equation.

Q. A man 4 times as old as his son. After 16 years, he will be only twice as old as his son. Find their present ages.

Q.

The length, breadth and height of a cuboidal reservoir is $7m,6m$ and $15m$ respectively. $8400$ L of water is pumped out from the reservoir. Find the fall in the water level in the reservoir.

Q. For the equation 3x+5=17, what will be the value of x?

1. $x=44$
2. $x=4$
3. $x=12$
4. $x=\frac{4}{3}$

Q. Find the degree of the equation : x² – 2x + 1 = x² – 3.

Q. It takes 20 minutes for pipe A to fill the tank completely and it takes 30 minutes for pipe B to fill the tank completely. If both the inlets are opened together, then how much time will be taken to fill the tank completely?

Q.

The total number of variables in the equation 3a + b + 6ab = 0 is 3. State True or False.

1. True

2. False

Q. Find the value of $x$ that satisfies the given equation.

$5x+10=26+x$

1. 4
2. 3
3. 15
4. 25

Q. 5 added to two times of a number gives 45. Find the number.

1. 10
2. 20
3. 30
4. 40

Q. Which of the following is/are not linear equation(s)?

1. $3x+5y-7z=2x^2$
2. $5y-7zx=29x+30$
3. $\frac{3x+7y}{9z+7x}=2$
4. $x-2x^2+3x^3=4$

Q. If $x=5$ satisfies the equation $2x-3=a$, then value of a is :

1. 8
2. 7
3. 5
4. 6

Q. A known quantity that has a fixed value is called:

1. variable
2. constant
3. expression
4. equation

Q. If LHS of an equation is $\frac{x-3}{2}$ and the solution of the equation is 6, then which of the following can be the RHS of this equation?

1. $\frac{x}{4}$
2. $\frac{x+6}{8}$
3. $\frac{9}{x}$
4. $\frac{3x}{2}$

Q. Choose the linear equations among these.

1. 2x + 4y - 7z = 9
2. 6p - 9q + r = 0
3. 2xy + 7xz - 9zy = 5
4. 4x + 6y - z

Q. The sum of a natural number and its reciprocal is $\frac{10}{3}$. Find the number

Q. Select the linear equations from the following equations.

1. $7p+6q+12s=5$
2. $xy+yz+zx=5$
3. $5x^2+6xy-4y^2=4$
4. $3x+2y-6=2$

Q. Solve each of the following equations and also check your results in each case:

(xix) $\frac{45-2x}{15}-\frac{4x+10}{5}=\frac{15-14x}{9}$

Q.

Question 2

In the following question out of the four options only one is correct, write the correct answer:
(a) $x=\frac{a}{b}$
(b) $x=-b$
(c) $x=\frac{-b}{a}$
(d) $x=\frac{b}{a}$
The solution of the equation ax+b=0 is:

Q.

Let Kanikas present age be x years, then Her fathers age exceeds her age by 35 years

Write expression

Q.

The sum of two numbers is $60$ and their difference is $30$.(a) If smaller number is $x$, the other number is _____ (b) The difference of numbers in term of $x$ is _____ (c) The equation formed is ______ (d) The solution of the equation is ______ (e) The numbers are _____ and ______ .

Q.

Solve the following equations and check the solutions obtained.

$3x-2=22$

Q.

There are 750 students in a school. If there are "x" boys and 110 more girls, then which of the following linear equation represents the same.

1. x + x +110= 750

2. 2x + 110 = 750

3. x + x = 750 + 110

4. 110x = 750

Q.

Simplify and solve the following linear equation

3(5z_7)_2(9z_11)=4(8z_13)_17

Q. If y = 11c + 4, then value of y if c = -2?

1. -16
2. -18
3. -11
4. -19

Q. Match the following equations with their degree.

1. 1
2. 5
3. 4
4. 2

Q.

Which of the following is a linear expression in one variable?

1. $x^2+3=0$

2. $xy+5$

3. $x+5=0$

4. $x+5$

Q.

Solve the equation $100x=400$ by the systematic method.

Q.

Will $t=1$ satisfy the equation $5t-4=1$?

1. No

2. Yes

Q.

Which of the following is a linear equation?

i) $x-2y=76$

ii) $x+78y^3=98$

iii) $x^2+2x-5=0$

iv) $x^2+2x+2=0$

1. a)

2. b)

3. d)

4. c)