Worksheet Questions (Part-1) - Linear Equations in One Variable

Introduction:
Linear equations in one variable are equations that involve a single variable raised to the power of 1, such as "x" or "y". These equations can be solved to find the value of the variable that satisfies the given equation. In this discussion, we will explore and explain the questions on a worksheet related to linear equations in one variable.

Question 1:
Solve the equation 3x + 5 = 14.

Solution:
To solve the equation 3x + 5 = 14, we need to isolate the variable "x" on one side of the equation. We can do this by performing inverse operations.

1. Subtract 5 from both sides of the equation:
3x + 5 - 5 = 14 - 5
3x = 9

2. Divide both sides of the equation by 3:
(3x)/3 = 9/3
x = 3

Therefore, the solution to the equation 3x + 5 = 14 is x = 3.

Question 2:
If 5 times a number is increased by 3, the result is 23. Find the number.

Solution:
Let's assume the number as "x". According to the given information, the equation can be written as 5x + 3 = 23.

1. Subtract 3 from both sides of the equation:
5x + 3 - 3 = 23 - 3
5x = 20

2. Divide both sides of the equation by 5:
(5x)/5 = 20/5
x = 4

Therefore, the number that satisfies the equation 5 times a number increased by 3 equals 23 is x = 4.

Question 3:
The sum of two consecutive odd integers is 56. Find the integers.

Solution:
Let's assume the first odd integer as "x". Since the integers are consecutive, the second odd integer can be expressed as (x + 2).

According to the given information, the equation can be written as x + (x + 2) = 56.

1. Simplify the equation:
2x + 2 = 56

2. Subtract 2 from both sides of the equation:
2x + 2 - 2 = 56 - 2
2x = 54

3. Divide both sides of the equation by 2:
(2x)/2 = 54/2
x = 27

Therefore, the two consecutive odd integers whose sum is 56 are 27 and 29.

Conclusion:
In this discussion, we have explained and solved three worksheet questions related to linear equations in one variable. By following the steps of isolating the variable and performing inverse operations, we were able to find the solutions to the given equations. It is essential to understand the concept of linear equations in one variable to solve such problems effectively.

X/3+3/2=-5/2