Solve the equation (2x – 3)2/3 = 4

Algebra is the branch of mathematics that includes numerals and variables with operators. The term that has constant value is known as numerals, it is represented by numbers. The term that does not have a constant value is known as the variable, its value is not fixed, it is represented by letters and symbols. Algebra is basically used to calculate the value of the unknowns. With the help of the information given in the question, we apply the operation and get the value of unknows.

Algebraic Expression

An algebraic expression is the representation of the mathematical statement into the mathematical form with the help of numerals, variables, and appropriate operators. 

For example: ‘Three times a number is added to 12’ can be written as ‘3x + 12’. Here we do not know the value of the number so we suppose it as x, it can take any value. Plus sign separate the statement into two-part, we name it as terms. In 3x + 12, there are two terms. 

So on the basis of the number of terms, the algebraic expression can be classified into the following types.

• Monomial: If the number of terms in the expression is one then it is known as a monomial. Example: 5x, 6y, etc
• Binomial: If the number of terms in the expression is two then it is known as binomial. For example: 5x+3, 12y-3, etc.
• Trinomial: If the number of terms in the expression is three then it is known as the trinomial expression. For example: 5x-6y+3z, 5q-6f+3x, etc.
• Polynomial: If the number of terms in an expression is one or more than one then it is termed as the polynomial.

Solution of an equation:

Earlier in this article, we said, variables can take any value. But when we compare an algebraic expression with numerals then these variables should have any fixed value. With the help mathematical operation, we can find the value of the variables. The solution of an equation is the value of numerals at which the given equation got satisfied. The left-hand side and right-hand side of the equation should have to equal.

Solve the equation (2x – 3)^2/3 = 4

Solution:

Step to solve the problem:

Step 1: To solve the exponent of an equation, do the inverse operation on both sides.

In the given problem, we can clearly see there is the cube root and square on the variable part so the inverse operation is the cube and square root respectively.

⇒ (2x – 3) = 4^(3/2)

⇒ (2x – 3) = (4³)^(1/2)

⇒ (2x – 3) = (64)^(1/2)

As we know that the square root of 64 is +8 and -8.

Step 2: Here we have two cases because the square root of 64 gives two values.

Case 1: When the square root is +8

⇒ 2x – 3 = 8

Case 2: When the square root is -8.

⇒ 2x – 3 = -8

Step 3: Transfer all the numerals on one side and all the variables on the other side of the equal sign. And get the value of the variables.

Case 1:

⇒ 2x – 3 = 8

⇒ 2x = 8 + 3

⇒ 2x = 11

⇒ x = 11/2

Case 2: 

⇒ 2x – 3 = -8

⇒ 2x = -8 + 3 

⇒ 2x = -5

⇒ x = -5/2

So the solutions of the given equation are x = 11/2 and x = -5/2.

Similar Questions

Question 1: Find all the solutions to the equation: (x – 2)^2/3 = 9.

Solution:

In the given problem, we can clearly see there is the cube root and square on the variable part so the inverse operation is the cube and square root respectively.

⇒ (x – 2) = 9^(3/2)

⇒ (x – 2) = (9³)^(1/2)

⇒ (x – 2) = (729)^(1/2)

So, the square root of 729 is -27 and +27. So we have two cases.

Case 1:

⇒ (x – 2) = 27

⇒ x = 27 + 2

⇒ x = 29

Case 2: 

⇒ (x – 2) = -27

⇒ x = -27 + 2

⇒ x = -25

So the solution of the given equation is x = +29 and x = -25.

Question 2: Find all the solutions to the equation: (3x – 2)^2/3 = 1.

Solution: 

In the given problem, we can clearly see there is the cube root and square on the variable part so the inverse operation is the cube and square root respectively.

⇒ (3x – 2) = 1^(3/2)

⇒ (3x – 2) = (1³)^(1/2)

⇒ (3x – 2) = 1^(1/2)

So, the square root of 1 is +1 and -1. So we have two cases.

Case 1:

⇒ 3x – 2 = 1

⇒ 3x = 1 + 2

⇒ 3x = 3

⇒ x = 1

Case 2: 

⇒ 3x – 2 = -1

⇒ 3x = -1 + 2

⇒ 3x = +1

⇒ x = 1/3

So the solution of the given question is  x = 1/3 and  x = 1.

Question 3: Find all the solutions to the equation: (7x + 4)^2/3 = 1.

Solution: 

In the given problem, we can clearly see there is the cube root and square on the variable part so the inverse operation is the cube and square root respectively.

⇒ (7x + 4) = 1^(3/2)

⇒ (7x + 4) = (1³)^(1/2)

⇒ (7x + 4) = 1^(1/2)

So, the square root of 1 is +1 and -1. So we have two cases.

Case 1:

⇒ 7x + 4 = 1

⇒ 7x = 1 – 4

⇒ 7x = -3

⇒ x = -3/7

Case 2: 

⇒ 7x + 4 = -1

⇒ 7x = -1 -4

⇒ 7x = -5

⇒ x = -5/7

So the solution of the given question is  x = -3/7 and  x = -5/7.