Step-by-Step Algebra Practice Problems for Better Understanding
Algebraic Equations are the equations obtained by equating to zero a sum of a finite number of terms, each of which is a product of positive integral powers, including the zero power of the variables. So in simple terms, Algebraic equations are polynomial equations. It is balanced as both sides have the same value. To avoid committing an error that tips the equation out of balance, make sure that any change on one side of the equation is reciprocated on the other side.
Let us solve some questions more understanding –
An Image of Algebraic Operations
Questions:
1. Find the solution of the one-step equation.
−16 + x = 15
18 + m = 8
2. Solve.
x + 1 = 9
3. State true or false.
The solution of the one-step equation p − 6 = −5 is -1.
4. Solve a one-step equation.
x - 7 = 10
n + 16 = 9
5. State true or false.
The solution of one-step equation 15 + b = 23 is 8.
6. Solve
5x = -15
7. Find the value of the variable:
−5 = a/18
21 = −7n
8. State true or false.
The solution of the one step equation x − 7 = 13 is 10.
9. Solve the one step equation.
10n = 40
v − 15 = −27
10. Solve.
2t = 200
11. Find the solution of the one step equation.
x + 9 = 8
−104 = 8x
12. Solve the equation.
m + 4 = −12
16 = k/11
13. State True or False.
The solution of one step equation x + 7 = 6 is x = -1.
14. Solve the one step equation.
y/7 = -2
−17x = −204
15. Find the value of the variable:
14b = −56
−143 = −11x
Answers:
1. −16 + x = −15
⇒ x = -15 + 16
⇒ x = 1
18 + m = 8
⇒ m = 8 - 18
⇒ m = -10
2. x + 1 = 9
⇒ x = 9 - 1
⇒ x = 8
3. False
p − 6 = −5
⇒ p = -5 + 6
⇒ p = 1
4. x - 7 = 10
⇒ x = 10 + 7
⇒ x = 17
n + 16 = 9
⇒ n = 9 - 16
⇒ n = -7
5. True
15 + b = 23
⇒ b = 23 - 15
⇒ b = 8
6. 5x = -15
⇒ x = -15/5
⇒ x = -3
7. −5 = a/18
⇒ a = -5 × 18
⇒ a = -90
21 = −7n
⇒ n = 21/-7
⇒n = -3
8. False
x − 7 = 13
⇒ x = 13 + 7
⇒ x = 20
9. 10n = 40
⇒ n = 40/10
⇒ n = 4
v − 15 = −27
⇒ v = -27 + 15
⇒ v = -12
10. 2t = 200
⇒ t = 200/2
⇒ t = 100
11. x + 9 = 8
⇒ x = 8 - 9
⇒ x = -1
−104 = 8x
⇒ x = -104/8
⇒ x = -13
12. m + 4 = −12
⇒ m = -12 - 4
⇒ m = -16
16 = k/11
⇒ k = 16 x 11
⇒ k = 176
13. True
x + 7 = 6
⇒ x = 6 - 7
⇒ x = -1
14. y/7 = -2
⇒ y = -2 × 7
⇒ y = -14
−17x = −204
⇒ x = -204/-17
⇒ x = 12
15. 14b = −56
⇒ b = -56/14
⇒ b = -4
−143 = −11x
⇒ x = -143/-11
⇒ x = 13
What is Algebra?
The broad area of mathematics where we study the symbols that represent a mathematical expression is called Algebra. This concept determines an unknown variable based on the questions asked. In simpler words, the concepts of Algebra enable us to define mathematical equations by using English letters such as x. y, z, etc.
Importance of Solving Equations Worksheet
Algebra needs a proper medium to be practised and imbibed well. For this, solving worksheets designed by subject experts can be very helpful for the students to grab hold of the mathematical principles.
The worksheet available on this page will be ideal for the students to solve and understand the concept faster. The problems are based on the mathematical principle of One Step Equations Algebra that students can easily identify and solve.
All the questions here can be solved if the students have followed how to create an equation and how to solve it. They will also use the fundamentals of mathematical operations and equivalence to solve an algebraic equation.
Hence, this worksheet will be the perfect guide to learning how to solve simple algebraic questions and find precise answers. Practising solving this worksheet will fortify the conceptual foundation of the students at this level to learn advanced algebraic concepts in the higher classes.
Benefits of One Step Linear Equations Worksheet
The questions set in this worksheet all focus on the principles of algebra for linear equations. You will learn how to easily apply the concepts of finding the answers to variables represented by English letters.
You will also get a good grip on the technique to solve these algebraic questions in no time. You will also learn to represent a variable with an English letter and form an equation on your own.
Resolve doubts related to these questions by referring to the solutions given in the worksheet. You will increase your knowledge and develop problem-solving skills for this topic.
Download One Step Algebra Equations Worksheets PDF
Get the free PDF version of these worksheets and complete your study material to learn this chapter well. Focus on how the experts have formulated the questions and take your preparation to the next level. Follow the solution to find out how the experts have compiled the answers to develop similar skills.
FAQs on Algebra Worksheet: Practice Key Algebra Concepts with Solutions
1. What is a variable in algebra, and how is it different from a constant?
In algebra, a variable is a symbol, typically a letter like 'x' or 'y', that represents an unknown or changeable value. A constant is a fixed number that does not change, like 7 or -15. For example, in the expression 4x + 7, 'x' is the variable, while '4' and '7' are constants.
2. What is the difference between an algebraic expression and an algebraic equation?
The main difference is the equals sign (=). An algebraic expression is a mathematical phrase combining numbers, variables, and operators (e.g., 5y - 3), which can be simplified or evaluated. An algebraic equation sets two expressions equal to each other (e.g., 5y - 3 = 12), creating a statement that can be solved to find the variable's value.
3. What does it mean to 'solve' an algebraic equation?
To 'solve' an algebraic equation means to find the specific numerical value of the variable that makes the statement true. This value is called the solution or root. For instance, in the equation x + 5 = 9, the solution is x = 4, because substituting 4 for x makes the equation true (4 + 5 = 9).
4. How do you form a simple algebraic equation from a word problem?
To form an equation from a word problem, follow these steps:
- Read the problem to identify the unknown quantity and represent it with a variable (like 'a').
- Translate the given information into mathematical operations (addition, subtraction, etc.).
- Set up a relationship of equality based on the problem's context using an equals sign.
5. Why is it essential to keep an equation balanced while solving it?
An equation represents a balance where the left side is equal to the right side. To maintain this truth, any mathematical operation performed on one side of the equation must also be performed on the other side. This principle, known as balancing, ensures that the equality remains valid, allowing you to correctly isolate the variable and find its accurate solution.
6. What is the main benefit of using an algebra worksheet for practice?
The primary benefit of solving an algebra worksheet is to reinforce conceptual understanding through targeted practice. Worksheets allow students to repeatedly apply rules and methods, which helps build speed, accuracy, and confidence. It is an effective way to test your grasp of a topic after studying the initial concepts from the textbook.
7. How is basic algebra used in real-world situations?
Basic algebra is frequently used in everyday life for problem-solving. Common examples include:
- Budgeting: Calculating how many items you can buy within a fixed budget.
- Cooking: Scaling a recipe up or down by adjusting ingredient quantities.
- Travel: Estimating arrival time using the formula Distance = Speed × Time.
- Health: Calculating calorie intake or determining a target heart rate during exercise.
