Solution of an Equation

Q.

Solve $2x+3y=11$and $2x-4y=-24$ and hence find the value of $m$ for which $y=mx+3.$

Q.

Each of the Boys were given a prize - Correct the sentence.

Q.

Question : 7

Which of the following equations has x = 2 as a solution?

(a) x + 2 = 5

(b) x - 2 = 0

(c) 2x + 1 = 0

(d) x + 3 = 6

Q.

Solve the sum of $8x+\frac{5}{2}=13$.

Q.

Question 4(d)

Complete the table and by inspection of the table find the solution to the equation m - 7 = 3.

$\begin{array}{cccccccccccc}m& 5& 6& 7& 8& 9& 10& 11& 12& 13& \cdots & \cdots \\ m-7& \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \end{array}$

Q.

If $m$ is a whole number less than $5,$ complete the table and by inspection of the table, find the solution of the equation $2m-5=-1$.

$\begin{array}{cccccc}m& & & & & \\ 2m-5& & & & & \end{array}$

Q.

Question 27

If $7x+4=25$, then the value of $x$ is ___ .

Q.

Question 52

Answer True/False.

$x=5$ is the solution of the equation $3x+2=20$.

Q.

Solve for $a$: $(a+4)+(a-2)=2$

1. -14

2. 0

3. 8

4. 14

Q.

In $-3x$, the literal factor is_______.

1. $1$

2. $-3$

3. $x$

4. $0$

Q.

A fruit grower can use two types of fertilizer in an orange grove, brand A and brand B.

Each bag of brand A contains $8$ pounds of nitrogen and $4$ pounds of phosphoric acid.

Each bag of brand B contains $7$ pounds of nitrogen and $7$ pounds of phosphoric acid.

Tests indicate that the grove needs $720$ pounds of nitrogen and $500$ pounds of phosphoric acid.

How many bags of each brand should be used to provide the required amounts of nitrogen and phosphoric acid?

Q.

Write four solutions for the given equation:

$x+\mathrm{\pi y}=4$

Q.

A truck can carry $x$ kg of weight. How much weight can $9$ trucks carry?

Q.

Question 4(b)

Complete the table and by inspection of the table find the solution to the equation 5t = 35.

$\begin{array}{ccccccccccccccc}t& 3& 4& 5& 6& 7& 8& 9& 10& 11& \dots & \cdots & \dots & \dots & \cdots \\ 5t& \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots \end{array}$

Q.

Question 9

Which of the following equations does not have a solution in integers ?

(a) $x+1=1$

(b) $x-1=3$

(c) $2x+1=6$

(d) $1-x=5$

Q.

Question 41

Answer True/False.

0 is a solution of the equation $x+1=0$.

Q.

Form the equation.

$15$ subtracted from thrice of a number.

Q.

Solve each of the following equations by trial and error method:

(ii) $2x+1=7$

Q.

Find the missing numbers that make the fractions equivalent.

$\frac{34}{51}=\frac{\square }{3}$

Q.

Write an algebraic expression for $2$ less than twice of $n$.

Q.

In natural numbers, $x–5=-5$ has _______ solution.

Q.

Simplify :

$\frac{8}{17}+\frac{3}{17}+\frac{1}{17}-\frac{11}{17}$

Q.

What are the properties of equality?

Q.

Which of the following equations cannot be formed using the equation x = 7?

(a) $2x+1=15$

(b) $7x-1=50$

(c) $x-3=4$

(d) $\frac{x}{7}-1=0$

1. (a)

2. (b)

3. ( c )

4. (d)

Q.

Sandeep was $p$years old $18$ years ago.

If $p=13$, how old is Sandeep now.

Q. If the sum of successor and predecessor of a number is 14, then the number should be _____.

1. 6
2. 8
3. 7
4. 10

Q.

Solve the following equations by trial-and-error method.

$\frac{2m}{7}=2$

Q. $P,Q$ and $R$ invested their capital in the ratio of $8:6:5$ at the end of the business they received the profit the ratio of $1:3:5.$ Find the ratio of time for which they contributed their capital?

1. $1:4:8$
2. $4:1:8$
3. $8:4:1$
4. $Ca{n}^{\prime }tbedetermined$

Q.

Question 72

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

Write two equations for which 2 is the solution.

Q. Match the following to find the value of x and y which balances the equations.

1. $x=3$
2. $y=3$
3. $x=6$
4. $y=5$