Linear equation in one variable

Q.

Question 1

In the following question out of the four options only one is correct, write the correct answer

The solution of which of the following equations is neither a fraction nor an integer?

(a) 3x + 2 = 5x + 2

(b) 4x – 18 = 2

(c) 4x + 7 = x + 2

(d) 5x – 8 = x + 4

Q. Which of the following pairs of equations have the same solutions?

1. 6x = 3 and 3x = 1.5
2. 8x = 3 and 4x = 1
3. 10x = 9 and 5x = 18
4. 12x = 6 and 6x = 6

Q.

The general form of equation in one variable is:

1. None of these

2. ax + b = 0

3. ax + b = 0 where a ≠ 0 and a, b are real numbers

4. ax + b = 0 where, a≠0

Q.

If the point (2k – 3, k + 2) lies on the line 2x + 3y + 15 = 0, find the value of k.

1. $k=\frac{-15}{7}$
2. $k=\frac{-13}{7}$
3. $k=\frac{15}{7}$
4. $k=\frac{13}{7}$

Q.

Find the value of 'x' in the equation $3x+8=0$.

1. $x=\frac{-8}{3}$

2. $x=\frac{8}{3}$

3. $x=-8$

4. $x=8$

Q.

When 14 is added to a number, we obtain 72. Which equation shows this relationship?

1. 14 – n = 72

2. 72n = 14

3. 72 + n = 14

4. 14 + n = 72

Q.

Which of the following is not a linear equation in one variable? (Consider a, b and c as constants and x as variable)

1. $ax+b=c$

2. $a^{3}x+b^2=c^4$

3. $abx+c=0$

4. $a{x}^4+b{x}^2+c=0$

Q. The pair of equations given by: y = 0 and y = -7, have ________.

1. no solution
2. two solutions
3. infinitely many solutions
4. unique solution

Q. If the amount of money with B is taken as ₹$b$, then thrice the amount of money B has will be ₹$3b$.

1. False
2. True

Q.

$x=-4$ is a solution to the equation $2x+8=0$

1. True

2. False

Q.

The solution of a linear equation is not affected when

1. The same numbers are added to both sides of the equation

2. We multiply or divide both the sides of the equation by the same non-zero numbers

3. We add a number to one side and subtract the same number from the other side of the equation

4. We multiply one side with a number and divide the same number from the other side of the equation

Q.

Write the following equations in word form.

a) 7x + 4=46

b) $\frac{5x+4}{6}=13$ [4 MARKS]

Q. If I have $x$ chocolates, what will be twice the number of chocolates I have?

1. $\frac{x}{2}$
2. $x+2$
3. $x^2$
4. $2x$

Q. The equations $2x+7=3$ and $bx-10=-2$ have the same solution for $x$. What is the value of $b$?

1. $-8$
2. $-2$
3. $4$
4. $-4$