Find y if 6y-8-6-8y = 4

Algebraic expression can also be termed variable expression. Algebraic expressions are considered equations where the variables are operated upon by operations such as addition, subtraction, multiplication, division. An algebraic expression is defined using the variables, constants which are integral values, and these terms are recognized with additional coefficients. For instance, the examples of algebraic expressions are 4x+1 = 0 and so on. 

The algebraic expressions can be simplified using substitution methods and simplification methods. The simplification method works where the number of variables is equivalent to the number of provided equations. The parts of the algebraic expression where the components are connected together using mathematical operations are known as algebraic terms. The algebraic expressions can be divided into various categories depending on the number of terms. An expression with a single term is called monomial, binomial, or trinomial. 

The below algebraic expression contains four terms, however, three of which can be easily connected together to form the variable part and constant part respectively. It is basically a linear equation with one variable where one equation is available. Therefore, on grouping the constant and variable part the equation can easily be simplified to obtain the solution in the following way: 

Question: Find y if 6y-8-6-8y = 4.

Solution: 

To determine the value of variable y. 

We have, 

6y – 8 – 6 – 8y = 4

On solving the constant part, we have, 

6y – 14 – 8y = 4 

Taking constants on the right hand side, 

6y – 8y = 4 + 14

6y – 8y = 18

-2y = 18

y = -18/2

y = -9 

Therefore, we obtain the value of y = -9

Sample Questions

Question 1: Explain the different types of terms contained in algebraic expressions.

Answer: 

1. Variables 

2. Constants

3. A combination of variables and constants joined using mathematical operations. 

Question 2: Define a polynomial.

Answer: 

An expression with one or more monomials is said to be a polynomial. The highest power of a variable is the degree of the polynomial. For instance, 3x+5y-2 = 0 is a polynomial. 

Question 3: Solve for 2z – 3 + z = 8

Solution: 

Simplifying the equation, we have, 

2z – 3 + z = 8 

3z = 5

z = 5/3

Therefore, z is equivalent to 5/3

Question 4: Solve for 

t + 7 = m – 2

2t – 2 = m + 12

Solution: 

Solving for first eq, we have, 

t = m + 5….I

Solving for second eq, we have, 

2t = m + 14…II

Now, 

Substituting the values of t = m + 5 

2(m + 5) = m + 14

Solving, we get, 

2m + 10 = m + 14 

Simplifying, 

m = 14 – 10 

m = 4 

Now, 

Substituting the value of m in I, we get, 

t = 4 +5 

t = 9

Question 5: Expand for the identity (a+b)²

Solution: 

On expanding (a+b)² , we get, 

a² + b² + 2ab