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

Q. The average of five consecutive even numbers is $54$. What is the difference between the highest and lowest numbers?

1. $5$
2. $6$
3. $8$
4. $10$

Q. Solve the following equations and check your results. If $\frac{2x}{3}+1=\frac{7x}{15}+3$, then $x$ is equal to

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

Q.

Write a pair of fractions whose sum is $\frac{8}{11}$ and difference is $\frac{2}{11}$.

Q.

Manuel ate $\frac{1}{3}$ of the cracker on a plate.

His brother ate $\frac{1}{4}$ of the cracker.

There were $5$ crackers left on the plate.

How many cracker were there to begin with?

Q. There are 80 balls in a bag. Some are red, some are green, and the remaining are blue balls. In the bag, $\frac{1}{4}$ of the total balls are blue and the number of red balls is twice more than green balls. Find the number of red balls in the bag.

1. 20
2. 15
3. 40
4. 30

Q.

Solve the following equations:

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

Q. The sum of three consecutive odd numbers is $63$. Find the numbers.

Q. Evalute:
$(9a-3a)+4a$

Q. If $M$ denotes $÷$, $L$ denotes $-$, $P$ denotes $\times$ and $J$ denotes $+$, then find the value of $25M5L10P2J15.$

1. $0$
2. $10$
3. $15$
4. $5$

Q. Arjun is twice as old as Shriya five years ago his age was three times Shriya's age. Find their present ages.

Q.

Solve: $\frac{3}{7}\mathrm{x}=\frac{20}{7}-\mathrm{x}$

Q. Cost of a book is ₹ x, then cost 8 such books will be ₹ 8x.

1. True
2. False

Q.

Equation $x/4=5$ is satisfied for the value of a variable $x=20$. True or False?

1. True
2. False

Q. $\text{The expression for the statement "One half of the sum of three and nine}$
$\text{is added to twelve" is}\frac{1}{2}\times (3+9)+12$

1. True
2. False

Q. When 'x' is replaced with '3', the equation x + 5 = 8 holds true.

1. No
2. Yes

Q. Solve the following equation for $x$.
$3(2x+1)+2(3x+1)=17$

1. $1$
2. $\frac{1}{2}$
3. $-1$
4. $2$

Q. Some students planned a picnic. The total budget for food was $Rs2000$. But $5$ students failed to attend the picinic and thus the cost of food for each member increases by $Rs20$. How many students attended the picinic and how much did each student pay for the food.

Q. Nimmi was asked to solve all these questions by her teacher.

(i) $2+\frac{3}{5}$

(ii) $5+\frac{1}{5}$

(iii) $1+\frac{4}{5}$


Help her solve these questions.

Q. Mayank saves ₹4000 from his salary. If this is $20\%$ of his salary, find his salary.

Q. You buy 50 pencils. You keep 10 for yourself and distribute the remaining pencils equally among your 8 friends. Which of the following expression gives the number of pencils that each person receives?

1. (50 - 8)/10
2. (50 - 10)/8
3. (50 + 10)/8
4. (10 + 8)/50

Q. Simplify : $[0.9-\{2.3-3.2-3.2-(7.1-5.4-3.5)\left\}\right]$

1. 0.18
2. 1.8
3. 0
4. 2.6

Q. Find the value of $x$ that satisfies the given equation.

$5x+10=26+x$

1. 4
2. 3
3. 15
4. 25

Q. Solve the following equation:

1. $-6$
2. $22$
3. $12$
4. $-15$

Q. In a cricket team the ratio of total number of players to the number of wicket keepers is

1. 1 : 11
2. 11 : 1
3. 16 : 1
4. 10 : 1

Q. Factorise: $100-a^2-b^2-2ab$.

Q. You buy 50 pencils. You keep 10 for yourself and distribute the remaining pencils equally among your 8 friends. Which of the following expression gives the number of pencils that each person receives?

1. (50 - 8)/10
2. (50 - 10)/8
3. (50 + 10)/8
4. (10 + 8)/50

Q. Which of the following gives the complete stem-and-leaf plot and the mean of the given data?


Number of pizza sold in 10 days : \( 68, 52, 56, 62, 78, 90, 86, 76, 75, 87 \) Number of pizza \( \text { Key } 5 \mid 2=52 \)

Q. $\text{The expression for the statement "One half of the sum of three and nine}$
$\text{is added to twelve" is}\frac{1}{2}\times (3+9)+12$

1. True
2. False

Q.

Q8 A certain amount was divided between Kavita and Reena in the ratio 4:3 . If Reena s share was RS 2400 then the amount is

Q. Number of integers in range of $x$ which satisfies the following: