Simplify (x-3)(3/4) + 1/8 = 0

In elementary classes, it was taught that letters are related to English or literature subject and numbers are related to mathematics. For example, a,b,c,d.. and so on are the letters of the English alphabet and 1,2,3,4… and so on is comes under mathematics. We did the basic arithmetic operation on numbers and calculate the value. But in middle school classes, letters are now used in mathematics subjects. These letters are used to represent the unknowns along with the numerals and operations, and this process is known as algebra. 

Algebraic Expression

An algebraic expression is the combination of numerals and variables along with the arithmetic operators. We use the algebraic expression to represent the mathematical statement into the expression.

For example, ‘Nine is taken away from a number’ that can be written as ‘x-9’. Here we don’t know the value of a number so we represent it by x. The negative sign separates the expression into two terms. So on the basis of the number of terms the expression can be classified into the following categories. 

• Monomial: If the number of terms in an expression is one then the expression is known as the monomial. Example: 5x,6y, etc.
• Binomial: If the number of terms in an expression is two then the expression is known binomial. Example: 8x-6, 3y+r, etc.
• Trinomial: If the number of terms in an expression is three then the expression is known as trinomial. Example: a-c+e, 8q-2j+3r, etc
• Polynomial: If the number of terms in an expression is one or more than one then the expression is known as the polynomial.

Algebraic Equation

When we compare an expression with the other expression then it is known as the algebraic equation. Algebraic equations consist of equalities signs. For example,

3x + 2 = 0

Here we are comparing 3x + 2 with 0, 3x + 2 and 0 is equal. 

In the algebraic equation, there are left-hand sides (LHS) and right-hand sides (RHS).

Find all the solutions to the equation. (x-3){3/4} + {1}/8} = 0

Solution:

Step to solve the problem: 

Step 1: Simplify the bracket part of the algebraic equation.

⇒ (x-3) × (3/4) + (1/8) = 0

Step 2: Do the calculation according to the operators.

⇒ 3x/4 – 9/4 + 1/8 = 0

Step 3: Transfer all the numerals part on one side and the variable part on the other side of the equation. If a term has the positive sign on the left side and we transfer it to the other side then its sign changed to negative, similarly the negative sign changes to positive, multiplication changes to division, and division changes to multiplication.

⇒ 3x/4 = 9/4 – 1/8

Step 4: Convert the numerals part into like fractions and solve them.

⇒ 3x/4 = 18/8 – 1/8

⇒ 3x/4 = (18 – 1)/8

⇒ 3x/4 = 17/8

⇒ x = (17 × 4)/(8 × 3)

Step 5: Cancel out the common factor.

⇒ x = 17/6

So the solution of the equation is x = 17/6.

Similar Question

Question 1: Find all the solutions to the equation. (a – 3)(5/6) – (9/7) = 0.

Solution:

Simplify the bracket part of the algebraic equation.

⇒ (a × 5)/6 – 3 × 5/6 – 9/7 = 0

⇒ 5a/6 – 5/2 – 9/7 = 0

Transfer all the numerals part on one side and the variable part on the other side of the equation. If a term has the positive sign on the left side and we transfer it to the other side then its sign changed to negative, similarly the negative sign changes to positive, multiplication changes to division, and division changes to multiplication.

⇒ 5a/6 = 5/2 + 9/7

 Convert the numerals part into like fractions and solve them.

⇒ 5a/6 = 35/14 + 18/14

⇒ 5a/6 = (35 + 18)/14

⇒ 5a/6 = 53/14

⇒ a = (53 × 6)/(14 × 5)

⇒ a = 159/35

So the solution of the equation is a = 159/35.

Question 2:  Find all the solutions to the equation. (9x – 3)(1/2) + 3/8 = 0

Solution:

Simplify the bracket part of the algebraic equation.

⇒ 9x×1/2 -3×1/2 + 3/8 = 0

Transfer all the numerals part on one side and the variable part on the other side of the equation. If a term has the positive sign on the left side and we transfer it to the other side then its sign changed to negative, similarly the negative sign changes to positive, multiplication changes to division, and division changes to multiplication.

⇒ 9x/2 = 3/2 – 3/8

 Convert the numerals part into like fractions and solve them.

⇒ 9x/2 = 12/8 – 3/8

⇒ 9x/2 = (12 – 3)/8

⇒ 9x/2 = 9/8

⇒ x = (9 × 2)/(8 × 9)

Cancel out the common factor.

⇒ x = 1/4

So the solution of the equation is x = 1/4.