- Rational Numbers
- Linear Equations in One Variable
- Understanding Quadrilaterals
- Practical Geometry
- Data Handling
- Squares and Square Roots
- Cubes and Cube Roots
- Comparing Quantities
- Algebraic Expressions and Identities
- Visualising Solid Shapes
- Mensuration
- Exponents and Powers
- Direct and Inverse Proportions
- Factorisation
- Introduction to Graphs
- Playing with Numbers
NCERT Solutions Class 8 Mathematics Solutions for Exercise 1.1 in Chapter 1 - Rational Numbers
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Verify that : -(-x) = x for.
(i) x=\frac{11}{15} (ii) x=-\frac{13}{17}
\text { (i) } x=\frac{11}{15}
We have, x=\frac{11}{15}
The additive inverse of x is –x (as x+(-x)=0)
Then, the additive inverse of \frac{11}{15} is \frac{-11}{15} \left(\operatorname{as} \frac{11}{15}+\left(\frac{-11}{15}\right)=0\right.
The same equality \frac{11}{15}+\left(\frac{-11}{15}\right)=0 shows that the additive inverse of \frac{-11}{15} \text { is } \frac{11}{15}
\begin{array}{l} \text { Or, }-\left(\frac{-11}{15}\right)=\frac{11}{15} \\ \text { i.e., }-(-x)=x \end{array}
\text { (ii) } x=-\frac{13}{17}
We have, x=-\frac{13}{17}
The additive inverse of x is –x (as x+(-x)=0)
Then, the additive inverse of \frac{-13}{17} \text { is } \frac{13}{17} \quad\left(\right.\text { as }\left(\frac{-13}{17}+\frac{13}{17}\right)=0
The same equality \left(\frac{-13}{17}+\frac{13}{17}\right)=0, \text { shows that the additive inverse of } \frac{13}{17} \text { is } \frac{-13}{17}
\begin{array}{l} \text { Or, }-\left(\frac{13}{17}\right)=\frac{-13}{17} \\ \text { i.e., }-(-x)=x \end{array}
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