Solving Equations with Linear Expressions on One Side and Numbers on the Other Side

Q.

$\frac{x}{3}+1=\frac{7}{15}$ Solve for $x$.

Q. The present age of pratik and arjun are in the ratio 2:3. 4 years from now, the ratio of their ages will be 4:5. What is the present age of Pratik?

Q.

$\frac{x}{5}+30=18$ has the solution as ______.

Q.

Two rectangles have different dimensions. Each rectangle has a perimeter of (7x + 5) inches. Draw and label diagrams that represent possible dimensions of the rectangles.

Q. how to solve x^2+3>0 by wavy curve method

Q. A part of monthly hostel charges in a college is fixed and the remaining depend on the number of days one has taken food in the mess. When a student A, takes food for 22 days, he has to pay Rs. 1380 as hostel charges, whereas a student B, who takes food for 28 days, pays Rs. 1680 as hostel charges. Find the fixed charge and the cost of food per day.

Q. Factorize: $121b^2+88bc+16c^2$

1. $(11b-4c{)}^2$
2. $(4b+11c{)}^2$
3. $(4b-11c{)}^2$
4. $(11b+4c{)}^2$

Q. Factorise: $x^2+\frac{1}{4x^2}+1-7x-\frac{7}{2x}$

1. $(x+\frac{9}{2x})(x+\frac{1}{2x}-3)$
2. $(x-\frac{2}{x})(x+\frac{1}{2x}-3)$
3. $(x+\frac{1}{2x})(x+\frac{1}{2x}-7)$
4. $(x-\frac{1}{x})(x+\frac{1}{2x}-7)$

Q. the set of values of x satisfying 2X-3/3x-5>3

Q.

Solve the following equations and check your result:

$\frac{2b}{3}-\frac{3b}{8}=\frac{7}{12}$

Q. Find the next term in the following series :

4, 2, 7, 5, 10, 8, __, __

1. 14, 16
2. 13, 11
3. 16, 18
4. 12, 10

Q. 5x+1/5x+1 + 2x = -2x , find the value of x.

Q. In an examination, there are three papers each of 100 marks. A candidate obtained 53 marks in the first paper and 75 marks in the second paper. How many marks must the candidate obtain in the third paper to get an overall of 70% marks?

Q. $x^2+3x+2+ax+2a$

1. $(3x-2)(x+a+2)$
2. $(3x+2)(x-a+1)$
3. $(x-2)(x+a-1)$
4. $(x+2)(x+a+1)$

Q. Write the linear equations in two variables for the given information :
A fraction becomes $\frac{9}{11}$ , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$.

Q.

What is the value of $2.\overline{6}-1.\overline{9}$

1. $0.\overline{6}$
2. $0.\overline{9}$
3. $0.\overline{7}$
4. $0.7$

Q. If U ={x | x ∈ N , x < 10} and A = {x | x ∈ N , 2 ≤ x < 6} then (A′)′ is:

a) {1, 6, 7, 8, 9}
b) Power set{1, 2, 3, 4}
c) {2, 3, 4, 5}
d) { }
$\left[1\right]$

Q. Solve the following inequality:
$\sqrt{2x-x^2}<5-x.$

Q. Solve :- $xy(y+10)dy=(x^2+1)dx$

Q. $(a+b{)}^2+9(a+b)+14$

1. $(a+b+2)(a+b+7)$
2. $(a+b+2)(a+b-7)$
3. $(a+b-2)(a+b+7)$
4. None of these

Q. If $x+y=10$ and $x-y=2$, then value of x is

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

Q. The value of $x$ satisfying the equation $x-\frac{7}{5}=\frac{13}{5}$ is___

Q.

Solve the given equation by systematic method$:$

$x+3=4\frac{1}{5}$

Q.

The present age of Vinay’s mother is three times the present age of Vinay. After 5 years, the sum of their ages will be 70 years. Find their present ages.

1. 10 years, 30 years

2. 20 years, 60 years

3. 15 years, 45 years

4. 18 years, 54 years

Q. Five years ago, Shikha was thrice as old as Rani. $10$ years later, Shikha will be twice as old as Rani. How old are they now?

1. Rani $20$ yrs, Shikha $50$ yrs
2. Shikha $20$ yrs, Rani $50$ yrs
3. Shikha $80$ yrs, Rani $30$ yrs
4. Shikha $30$ yrs, Rani $80$ yrs

Q.

The present age of Vinay’s mother is three times the present age of Vinay. After 5 years, the sum of their ages will be 70 years. Find their present ages.

1. 15 years, 45 years

2. 10 years, 30 years

3. 20 years, 60 years

4. 18 years, 54 years

Q. The value of $x$ satisfying the equation $x-\frac{7}{5}=\frac{13}{5}$ is___

Q. A train travels 360 km at a uniform spped. If the speed had been 5km/h more, it would have taklen 1 hour less for the same journey.Find the speed of the train.