Transposing Method

Q.

Solve the following equation: $\frac{3}{7}+x=\frac{17}{7}$

Q.

When you subtract 10 from thrice a number, the result is 17. Find the unknown number. [2 MARKS]

Q. A can do a piece of work in 6 days and B can do it in 8 days .
How long will they take to complete it together ?

Q. The difference between two integers is 75. If the larger number is divided by the smaller number, then the result is 4. Find the two integers.

1. 40, 160
2. 20, 80
3. 30, 105
4. 25, 100

Q.

Choose the correct answer in the given question.

Latika is $6m$ years old. She is thrice as old as her sister. What will be their ages after six years?

1. $8m+6$

2. $8m+12$

3. $24m+6$

4. $24m$

Q. Consider the equation, $\frac{x}{2}=5$. If 2 is transposed from LHS to RHS, then it becomes in the RHS.

1. $\times 2$
2. $÷2$
3. $+2$
4. $-2$

Q.

Solve the following equation by transposing the terms and check your result:
$3y+4=5y-4$

Q. Which of the following equations has solution x = -2?

1. 2x = -6
2. x + 3 = 5
3. 3 - x = 5
4. 2x = - 1

Q. Simplify:
${(-3)}^2\times {(-5)}^2$

Q. What is/are the correct step(s) to solve the following equation?
$2x+7=12-3x$

1. $2x+3x=12-7$
2. $2x-3x=12+7$
3. $-2x+3x=-12-7$
4. $-2x-3x=7-12$

Q. In the following equation,
$(a+bx)-(cx-d)=mx$, the value of $x$, is

1. $-\frac{(a+d)}{(b-c+m)}$
2. $\frac{(a+d)}{(b-c-m)}$
3. $\frac{(a-d)}{(b+c-m)}$
4. $-\frac{(a+d)}{(b-c-m)}$

Q. In an isosceles triangle, the equal sides measure 4x - 1 and x + 5 units. The value of x is ___ units.

1. 1
2. 2
3. - 1
4. - 2

Q. The weight of Rahul is 5 kg more than Sachin. The weight of Samir is 12 kg less than double the weight of Sachin. if the total weight of all the three is 93. Form an equation for the given data.

Q.

When we divide two integers, we get can a/an _____.

1. 0 was exactly at the center of the number line

2. 0 was one of the integers

3. 0 was lesser than all the positive integers and greater than all the negative integers

4. Any two positive and negative integers will add up to 0

Q. Consider an equation,
$3x+4=7x-8$.
Which of the following can be the first step(s) to be followed to solve the equation?

1. $3x+4=7x-8$
2. $3x+4-7x=-8$
3. $4=7x-8-3x$
4. $3x-7x=-8+4$

Q. David cuts a cake into two equal halves. He cuts one half into smaller pieces of equal size. Each of these small pieces weighs twenty grams. If he has seven pieces of the cake in total, then how heavy was the original cake?

1. 120 grams
2. 180 grams
3. 300 grams
4. 240 grams

Q. If $(2x+3{)}^2+(2x-3{)}^2=(8x+6)(x-1)+22$, then the value of '$x$'

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

Q. What must be added to $\frac{x}{y}$ to make it $\frac{y}{x}$?

1. $\frac{y^2-x^2}{yx}$
2. $\frac{y-x}{y^2{x}^2}$
3. $\frac{xy}{x+y}$
4. $\frac{x^2-y^2}{x^2+y^2}$

Q.

Find the value of x in the equation $\frac{2}{5}+x=\frac{3}{5}.$

1. 1

2. $\frac{1}{5}$

3. $\frac{-1}{5}$

4. -1

Q.

$\text{Solve for x:}$

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

1. 3

2. 4

3. 5

4. 6

Q.

$\text{Solve for x.}$

$15-2(5-3x)=4(x-3)+13$

1. -2

2. 2

3. 1

4. -1

Q. A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 5 per bag of grey cement sold.
What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6, 400 bags?

Q. Solve for x:
$\frac{x}{7}+\frac{2}{7}=\frac{6}{7}$

1. 1
2. 4
3. 14
4. 9

Q. Find the value of (B-D) in the following equation.
$(Ax+By)+(Cx-Dy)=Ex-F$

1. $\frac{-F-(B-D)y}{(A+C-E)}$
2. $\frac{-F-(A+C-E)x}{y}$
3. $\frac{-F-(A+C-E)y}{x}$
4. $\frac{-F+(D-B)x}{(A+C-E)}$

Q.

Solve the equation $\frac{3}{x+1}=\frac{6}{5x-1}$.

1. 9

2. 1

3. 2

4. 3

Q. If $\frac{x+b}{7}=2,$ and $b=2$, then the value of $x$ is

1. 14
2. 16
3. 10
4. 12

Q. $\text{Solve for x:}$

$\frac{x}{a}+\frac{x}{b}=1$

1. $\frac{(a+b)}{ab}$
2. $\frac{b}{a+b}$
3. $\frac{(a+b)}{b}$
4. $\frac{ab}{a+b}$

Q. What must be subtracted from each term of the ratio 4:7, so that the ratio becomes 2:9?

1. $\frac{44}{7}$
   
2. $\frac{50}{7}$
3. $\frac{30}{7}$
4. $\frac{22}{7}$

Q. Consider an equation,
$\frac{24x}{y}-5=31x-\frac{5}{y}$
Which of the following step(s) is/are valid?

1. $\frac{24x}{y}+\frac{5}{y}=5+31x$
2. $\frac{24x}{y}+\frac{5}{y}-5=31x$
3. $-31x+\frac{24x}{y}=5+\frac{5}{y}$
4. $\frac{24x}{y}-5-31x+\frac{5}{y}=0$

Q. Find the solution of 2x – 3 = 7.