Variable on Both Sides

Q.

Solve for $2x+5y=\frac{8}{3}$and $3x-2y=\frac{5}{6}$

Q.

The value of variables which equates the LHS and RHS of the equation is called solution of the equation.

1. False

2. True

Q. y=[2x-1]=3[x-6] then find the possible values of [3x+y]

Q. 4x-7-(x+4)=3x+4-(2x-1)

Q.

Anita thinks of a number and subtracts $\frac{3}{2}$ from it. She multiplies the result by 8. The result now obtained is 5 times the number she thought of. Find the number.

1. 4

2. 6

3. 8

4. 10

Q.

$\text{Solve the following equation for}x\text{.}$
$\frac{5x-4}{6}=2+\frac{3x}{2}$

1. - 3

2. 2

3. 4

4. - 4

Q.

Can you show me the way to solve

Fill in the blanks

-2/9=?/63=?/81

Q.

The altitude of a triangle is three-fifth the length of its base. If the altitude is increased by 4 cm and the base is decreased by 2 cm, the area of the triangle remains the same. Find the base of the triangle in cm. [Area of triangle = $\frac{1}{2}\times \text{base}\times \text{height}$]

1. 50/14

2. 30/14

3. 20/14

4. 40/14

Q.

Solve and check result: 8x + 4 = 3(x − 1) + 7

Q.

Find x fothefollowing equation

{2+x}{7-x}{5-x}{4+x}=1

Q. Question 1
Amina thinks of a number and subtracts $\frac{5}{2}$ from it. She multiplies the result by 8 .The result now obtained is 3 times the same number she thought of. What is the number?

Q.

Solve:

Q.

$\text{If}3(3x+5)+12=2(x+3),\text{then find the value of}x.$

1. 3

2. - 3

3. 6

4. - 6

Q.

4z+3=6+2z

Q. If 3^x-1= 9 and 4^y+2 = 64, find the value of y/x - x/y.

Q.

Solve $3x^2+13x+10=0$.

Q.

The distance between two stations is 340 km. Two trains start simultaneously from these stations on parallel tracks and cross each other. The speed of one of the them is greater than that of the other by 5 km/hr. If the distance between two trains after 2 hours of their start is 30 km. find the speed of each train.

Q.

A Rational number is such that when you multiply it by 5/2 and add 2/3 to the product you get - 7/12 .what is the number?

Q.

The value of x for the equation 3(x + 3) = 5(x - 5) also satisfies the equation ______.

1. 2x - 17 = 0

2. 2x + 17 = 0

3. x + 17 = 0

4. x - 17 = 0

Q.

The altitude of a triangle is three-fifth the length of its corresponding base. If the altitude is increased by 4 cm and the base is decreased by 2 cm, then the area of the triangle remains the same. Find the base of the triangle in cm.

1. $3\frac{5}{7}$

2. $2\frac{5}{7}$

3. $2\frac{6}{7}$

4. $3\frac{6}{7}$

Q.

Solve the equations:

(i) 5x = 3x + 24;

(ii) 8t + 5 = 2t − 31;

(iii) 7x − 10 = 4x + 11;

(iv) 4z + 3 = 6 + 2z;

(v) 2x − 1 = 14 − x;

(vi) 6x + 1 = 3(x − 1) + 7;

(vii) ;

(viii) ;

(ix) 3(x + 1) = 12 + 4 (x − 1);

(x) 2x − 5 = 3(x − 5);

(xi) 6(1 − 4x) + 7(2 + 5x) = 53;

(xii) 3(x + 6) + 2 (x + 3) = 64;

(xiii) ;

(xiv) .

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

(xviii) $\frac{4x}{9}+\frac{1}{3}+\frac{13x}{108}=\frac{8x+19}{18}$

Q.

Solve for $x$:
$2x+5=3(x+2)$

1. -1

2. 3

3. 1

4. -2

Q.

Solve for $xandy$

$\frac{3x-2}{3y+7}=\frac{5x-1}{5y+16};\frac{3x-15}{x-9}=\frac{6y-5}{2y+3}$

Q.

Question 15

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

The sum of three consecutive multilpes of 7 is 357. Find the smallest multiple.

(a) 112

(b) 126

(c) 119

(d) 116

Q. Solve $\frac{22-4x}{3}=x-9$

Q.

The denominator of a rational number is greater than its numerator by 3. If the numerator is increased by 7 and the denominator is decreased by 1, then the new number becomes $\frac{3}{2}$. Find the original number.

1. $\frac{8}{11}$

2. $\frac{7}{10}$

3. $\frac{5}{8}$

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

Q. Solve the following equations:

(1) x + 1 = 6
(2) x + 4 = 3
(3) x − 3 = 5
(4) 2x = 8
(5) $\frac{a}{3}=7$
(6) 5a = − 20

Q. Solve:
$\frac{9x}{7-6x}=15$

Q.

Shalini was asked to solve a problem on the board. While solving the problem she made a silly mistake. Find the correct answer.
Question: Find the value of the expression $x^3-6x+7$ when x = -3
Step i: $(-3{)}^2-6(-3)+7$
step ii: - 27 - 9 + 7
step iii: - 29

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