Algebra help for free
Introduction :
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. In algebra, symbols are used to represent numbers or variables in arithmetical operations. An equation is an expression in algebra. Elementary algebra consists of methods of manipulating equations to put them in a more convenient form.
Examples
Ex 1: Simplify the expression (x - 17) + 4x = 10 + 3x
Sol: Given expression is (x - 17) + 4x = 10 + 3x
Step 1: Expand the above expression, we get
x - 17 + 4x = 10 + 3x
5x - 17 = 10 + 3x
Step 2: Subtract (10 + 3x) on both the side of the equation, we get
2x - 27 = 0
Step 3: Add 27 on both the sides, we get
2x = 27
Step 4: Divide the above equation by 2, we get
x = `(27 / 2)`
The final answer is x = `(27 / 2)`
Ex 2: Simplify the given expression (x + 3) + 2x = 12 - 2x
Sol: Given expression is (x + 3) + 2x = 12 - 2x
Step 1: Expand the above expression, we get
x + 3 + 2x = 12 - 2x
3x + 3 = 12 - 2x
Step 2: Subtract (12 - 2x) on both the side of the equation, we get
5x - 9 = 0
Step 3: Add 9 on both the sides, we get
5x = 9
Step 4: Divide the above equation by 5, we get
x = (9/5)
The final answer is x = (9/5)
Ex 3: Solve the given linear equation y - 34 = 12 + 2y
Sol: Given linear equation is y - 34 = 12 + 2y
Step 1: Subtract (12 + 2y) on both the sides, we get
- y - 36 = 0
Step 2: Add y 0n both the sides, we get
y = - 36
The final answer is - 36
Ex 4: Solve the given equation 10x - 35 = 25 for finding the value of x. Sol: Given equation 10x - 35 = 25
Step 1: Add 35 on both the sides of the above equation, we get
10x = 25 + 35
Step 2: Adding the two values 25 and 35, we get
10x = 60
Step 3: Divide by 10 on both the sides, we get
x = 6
The final answer is x = 6
Practice problems
Pro 1: Expand the given expression (x - 3) + 2x + 5 = 11 and find the value of x.
Ans: x = 3
Pro 2: Solve the linear function 2y = 9 - x and x + 3y = 13
Ans: x = 1, y = 4
Pro 3: Solve the linear function y + 12 = x and 2x + y = 12
Ans: x = 8, y = - 4
Pro 4: Find the value of y from the given expression (y + 10) - 4 = 23
Ans: The final answer is y = 17
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. In algebra, symbols are used to represent numbers or variables in arithmetical operations. An equation is an expression in algebra. Elementary algebra consists of methods of manipulating equations to put them in a more convenient form.
Examples
Ex 1: Simplify the expression (x - 17) + 4x = 10 + 3x
Sol: Given expression is (x - 17) + 4x = 10 + 3x
Step 1: Expand the above expression, we get
x - 17 + 4x = 10 + 3x
5x - 17 = 10 + 3x
Step 2: Subtract (10 + 3x) on both the side of the equation, we get
2x - 27 = 0
Step 3: Add 27 on both the sides, we get
2x = 27
Step 4: Divide the above equation by 2, we get
x = `(27 / 2)`
The final answer is x = `(27 / 2)`
Ex 2: Simplify the given expression (x + 3) + 2x = 12 - 2x
Sol: Given expression is (x + 3) + 2x = 12 - 2x
Step 1: Expand the above expression, we get
x + 3 + 2x = 12 - 2x
3x + 3 = 12 - 2x
Step 2: Subtract (12 - 2x) on both the side of the equation, we get
5x - 9 = 0
Step 3: Add 9 on both the sides, we get
5x = 9
Step 4: Divide the above equation by 5, we get
x = (9/5)
The final answer is x = (9/5)
Ex 3: Solve the given linear equation y - 34 = 12 + 2y
Sol: Given linear equation is y - 34 = 12 + 2y
Step 1: Subtract (12 + 2y) on both the sides, we get
- y - 36 = 0
Step 2: Add y 0n both the sides, we get
y = - 36
The final answer is - 36
Ex 4: Solve the given equation 10x - 35 = 25 for finding the value of x. Sol: Given equation 10x - 35 = 25
Step 1: Add 35 on both the sides of the above equation, we get
10x = 25 + 35
Step 2: Adding the two values 25 and 35, we get
10x = 60
Step 3: Divide by 10 on both the sides, we get
x = 6
The final answer is x = 6
Practice problems
Pro 1: Expand the given expression (x - 3) + 2x + 5 = 11 and find the value of x.
Ans: x = 3
Pro 2: Solve the linear function 2y = 9 - x and x + 3y = 13
Ans: x = 1, y = 4
Pro 3: Solve the linear function y + 12 = x and 2x + y = 12
Ans: x = 8, y = - 4
Pro 4: Find the value of y from the given expression (y + 10) - 4 = 23
Ans: The final answer is y = 17