Property of Equality

Q.

Solve the linear equation

$x+7-\frac{8x}{3}=\frac{17}{6}-\frac{5x}{2}$

Q. The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. What is the lowest score?

1. 44
2. 33
3. 40
4. 53

Q.

$\frac{4}{5}$ of a number is $5$ more than $\frac{3}{4}$ of the number. Find the number.

Q.

Question 74

Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:

Write an equation whose solution is not a whole number.

Q. $3x-51=5x-5$
Find the value of $x$ which satisfies the given equation ?

1. 42
2. -23
3. -25
4. 24

Q. What are the steps to be followed in order to solve this equation?

$\frac{x+3}{8}=\frac{1}{4}$

1. Subtract 3 from both the sides and then multiply both sides by 8.
2. Add 3 to both the sides and then divide both the sides by 8.
3. Multiply both sides by 8 and then subtract 3 from both sides.
4. Divide both the sides by 3 and then add 8 to both sides.

Q. The expression obtained when $x$ is multiplied by 2 and then subtracted from 3 is _______.

1. $2x-3$
2. $2x+3$
3. $3-2x$
4. $3x-2$

Q. Which of the following are not a valid operation on an equation?

1. Multiplying both sides of an equation with a number.
2. Adding 5 to the LHS and subtracting 5 from the RHS.
3. Dividing both sides by the same variable.
4. Dividing LHS by x and RHS by y.

Q.

Solve the following linear equation:

$x+7-\frac{8x}{3}=\frac{17}{6}-\frac{5x}{2}$

Q.

Which of the following equations has a solution of x = 3?

1. $8x-10=2x-16$

2. $7x=28$

3. $2x-3=3x-6$

4. $5x=15$

Q.

$\frac{x}{2}-\frac{x}{3}=\frac{x}{4}+\frac{1}{2}$. Solve it.

Q. The given equation is $2x+4=10$. If 4 is subtracted from the left-hand then what should be subtracted from the right-hand side to maintain the equality?

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

Q.

Solve the following equation:
$\frac{x}{3}=7$

Q.

Solve the equation. Check your solution.

$4x=36$

Q. Solve the following equation for the value of $x.$

$\frac{x}{3}-\frac{x}{4}=\frac{1}{2}$

1. 3
2. 6
3. 2
4. 1

Q. Solve the following equation for the value of $x.$

$\frac{x}{3}-\frac{x}{4}=\frac{1}{2}$

1. 3
2. 1
3. 6
4. 2

Q. If $\frac{2}{5x}-\frac{5}{3x}=\frac{1}{15}$, then the value of '$x$' is

1. 19
2. - 19
3. 43
4. 39

Q. What are the steps to be followed in order to solve this equation?

$\frac{x+3}{8}=\frac{1}{4}$

1. Subtract 3 from both the sides and then multiply both sides by 8.
2. Add 3 to both the sides and then divide both the sides by 8.
3. Multiply both sides by 8 and then subtract 3 from both sides.
4. Divide both the sides by 3 and then add 8 to both sides.

Q. The expression obtained when $x$ is multiplied by 2 and then subtracted from 3 is _______.

1. $2x-3$
2. $2x+3$
3. $3-2x$
4. $3x-2$

Q.

Simplify the algebraic fraction : $1\frac{\mathrm{x}}{2}+2\frac{2\mathrm{x}}{3}-\frac{\mathrm{x}}{6}$

Q. The expression obtained when $x$ is multiplied by 2 and then subtracted from 3 is _______.

1. $2x-3$
2. $2x+3$
3. $3-2x$
4. $3x-2$

Q.

Simplify the algebraic expression $\frac{\mathrm{x}}{2}÷(2\frac{2}{3}\mathrm{x}÷1\frac{5}{8}\mathrm{x})$ in its simplest form :

Q. Sort the following operations done on both sides of the equation, $\frac{2x-3}{3}-2=5$, to get the solution.

1. Add 2
2. Add 3
3. Divide by 2
4. Multiply by 3

Q. To get the value of $x$ in the equation, $x-3=6$, $3$ has to be subtracted from both sides of the equation.

1. True
2. False