Give an expression equivalent to 1 × (7x) = 52

Algebra is a discipline of mathematics that deals with mathematical expressions made up of constants and symbols. These symbols or letters used in these expressions are the representation of unknown values. These expressions are solved with certainly given formulas to derive a solution for unknown quantities.

Algebraic expression and formulae

Algebraic formulae are the standard equations that are built by the combination of symbols or letters and integers. The integers are the fixed values that cannot be changed and the letters stand for unknown values which are manipulated to derive a solution for the expression.

Algebraic expressions are made of terms that include constants, variables, and coefficient of variables as their components.

• Constants: The fixed integers present in the expression are the constants. These constants are always attached to a mathematical operation.
• Variable: Variables are the symbols or letters present in the expression which represents the unknown values of the expression.
• Coefficient: Coefficients are the real numbers attached to the variables in the expression.

Give an expression equivalent to 1 × (7x) = 52

Solution:

The given expression

1 × (7x) = 52 ⇢ (i)

Now, solving the equation (i) for the value of ‘x’.

1 × (7x) = 52

x = 52/7

x = 7.42

Then, To determine an expression equivalent to equation (i) we have to multiply both sides of the equation (i) by 2,

2(7x) = 52 × 2 

2(7x) = 104 ⇢ (ii)

Solving the equation (ii) for the value of ‘x’

2(7x) = 104

14x = 104

x = 104/14

x = 7.42

Thus, by equations (i) and (ii) can be proved to be equivalent expressions.

Sample Problems

Question 1: Write the equivalent expression for the given expression 2x(3y + 1).

Solution:

The given expression

2x(3y + 1)

Multiplying  the components in the bracket by 2,

x(6y + 2) 

Question 2: Write the equivalent expression for the given expression 3(x + 2y).

Solution:

The given expression

3(x + 2y)

Multiplying the components in the bracket by 3.

3x + 6y

Question 3: Write the equivalent expression for the given expression 2x + 4.

Solution:

The given expression

2x + 4

Taking 2 as common from both terms of the expression,

2(x + 2)

Question 4: Write the equivalent expression for the given expression 12x + 4.

Solution:

The given expression

12x + 4

Taking 4 as common from both terms of the expression,

4(3x + 1)