Write 'T' for true and 'F' for false for each of the following:
(i) (5 − 3x2) is a binomial.
(ii) −8 is a monomial.
(iii) (5a − 9b) − (−6a + 2b) = (−a − 7b).
(iv) When $x=2$ and $y=1$, the value of $\frac{-8}{7} x^{3} y^{4}$ is $\frac{-64}{7}$.
(v) $\frac{x}{4}+\frac{x}{6}-\frac{x}{2}=\frac{3}{4} \Rightarrow x=-9$.
(vi) $2 x-5=0 \Rightarrow x=\frac{2}{5}$.
(i) T
Binomial expression is an expression that shows the sum or the difference of two unlike terms. The above expression has two unlike terms, i.e. 5 and 3x2.
(ii) T
Any expression that contains only one term is called a monomial. It can either be a constant or a variable.
(iii) F
L. H. S. $=(5 a-9 b)-(-6 a+2 b)$
$=5 a-9 b+6 a-2 b=(-a-7 b)$
$=5 a+6 a-9 b-2 b=(-a-7 b)$
$=(11 a-11 b)$
This is not equal to $(-a-7 b)$.
Thus, the L.H.S. is not equal to the R.H.S.
(iv) T
$\frac{-8}{7} x^{3} y^{4}$
Given:
$x=2$
$y=1$
Given expression $=\frac{-8}{7}(2)^{3}(1)^{4}$
$=\frac{-8}{7} \times 8 \times 1$
$=\frac{-8}{7} \times 8 \times 1$
$=\frac{-64}{7}$
(v) T
$\frac{x}{4}+\frac{x}{6}-\frac{x}{2}=\frac{3}{4}$
$\Rightarrow \frac{3 x+2 x-6 x}{12}=\frac{3}{4}$
$\Rightarrow \frac{-x}{12}=\frac{3}{4}$
$\Rightarrow-4 x=36$
$\Rightarrow x=-\frac{36}{4}$
$\Rightarrow x=-9$
(vi) F
$2 x-5=0$
$\Rightarrow 2 x=5$
$\Rightarrow x=\frac{5}{2}$