Question

If $x=1.4$, find the value of $27\left(x+1.2\right)-26\left(x+1.2\right)$

(A) 1 (B) $-0.4$ (C) $2.6$ (D) $65$

Short answer

Correct option is (C) 2.6

Step-by-step solution

- Properties of real number

Properties of real numbers are written in following table:

For any real numbers a, b, and c:
Property	Addition	Multiplication
Commutative	a+b=b+a	$a·b=b·a$
Associative	$\left(a+b\right)+c=a+\left(b+c\right)$	$\left(a·b\right)·c=a·\left(b·c\right)$
Identity	a+0=a=0+a	$a·1=a=1·a$
Inverse	$a+\left(-a\right)=0=\left(-a\right)+a$	If $a\ne 0$, then $a·\frac{1}{a}=1=\frac{1}{a}·a$
Distributive	$a\left(b+c\right)=ab+ac\text{and}\left(b+c\right)a=ba+ca$

- Substitution

Substitute 1.4 for x in given expression

$27\left(1.4+1.2\right)-26\left(1.4+1.2\right)$

- Simplify 

To evaluate given expression, firstly use distributive property $ba+ca=\left(b+c\right)a$ then simplify terms in parentheses as show below

$\begin{array}{c}27\left(1.4+1.2\right)-26\left(1.4+1.2\right)=\left(27-26\right)\left(1.4+1.2\right)\\ =\left(1\right)\times \left(2.6\right)\\ =2.6\end{array}$

Thus, correct option is (C)