Question

Verify $a - ( - b) = a + b$ for the following values of $a$ and $b$.
(a) $a = {\text{ }}21,{\text{ }}b = {\text{ }}18$
(b) $a = {\text{ }}118,{\text{ }}b{\text{ }} = 125$
(c) $a = {\text{ }}75,{\text{ }}b = {\text{ }}84$
(d) $a = {\text{ }}28,{\text{ }}b{\text{ }} = {\text{ }}11$

Answer 1

Hint: According to the properties of algebra we know that the following statements are true: In an algebraic expression + and – becomes – , In an algebraic expression + and + becomes + , In an algebraic expression - and – becomes +.

Complete step by step answer:
A number line can help you to visualise both positive and negative numbers and the operations (adding and subtracting) that you can do with them. When you have an addition or subtraction to calculate, you start at the first number and move the second number of places either to the right (for an addition) or left (for a subtraction).This number line is a simplified version, but you can draw them with every number included

We will prove this equation by solving the question in two subheadings i.e. LHS and RHS as follows:
(a) To verify that $a - ( - b) = a + b$
$a = {\text{ }}21,{\text{ }}b = {\text{ }}18$
$\Rightarrow LHS=a - ( - b)$
$\Rightarrow LHS=21 - ( - 18)$
$\Rightarrow LHS=21 + 18$
We get the answer $39\;$
$RHS= a + b$
$\Rightarrow RHS= 21 + 18$
We get the answer $39\;$
Therefore, $a - ( - b) = a + b$
Hence verified.

(b) To verify that $a - ( - b) = a + b$
$a = {\text{ }}118,{\text{ }}b{\text{ }} = 125$
$LHS= a - ( - b)$
$\Rightarrow LHS= 118 - ( - 125)$
We get the answer $243\;$
$RHS=a + b$
$\Rightarrow RHS=118 + 125$
We get the answer $243\;$
Therefore, $a - ( - b) = a + b$
Hence verified.

(c) To verify that $a - ( - b) = a + b$
$a = {\text{ }}75,{\text{ }}b = {\text{ }}84$
$LHS=a - ( - b)$
$\Rightarrow LHS =75 - ( - 84)$
We get the answer $159\;$
$RHS=a + b$
$\Rightarrow RHS=75 + 84$
We get the answer $159\;$
Therefore, $a - ( - b) = a + b$
Hence verified.

(d) To verify that $a - ( - b) = a + b$
$a = {\text{ }}28,{\text{ }}b{\text{ }} = {\text{ }}11$
$LHS =a - ( - b)$
$\Rightarrow LHS =28 - ( - 11)$
We get the answer $39\;$
$RHS=a + b$
$\Rightarrow RHS=28 + 11$
We get the answer $39\;$
Therefore, $a - ( - b) = a + b$
Hence verified.

Note:We have to prove the question by showing both sides of the calculation. If two positive numbers are multiplied together or divided, the answer is positive. If two negative numbers are multiplied together or divided, the answer is positive. If a positive and a negative number are multiplied or divided, the answer is negative.