Question

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 $\frac{-8}{7}{x}^3{y}^4\mathrm{is}\frac{-64}{7}.$
(v) $\frac{x}{4}+\frac{x}{6}-\frac{x}{2}=\frac{3}{4}\Rightarrow x=-9.$
(vi) $2x-5=0\Rightarrow x=\frac{2}{5}.$

Answer 1

(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

$$\begin{gathered} \mathrm{L}.\mathrm{H}.\mathrm{S}.=\left(5a-9b\right)-\left(-6a+2b\right) \\ =5a-9b+6a-2b=\left(-a-7b\right) \\ =5a+6a-9b-2b=\left(-a-7b\right) \\ =\left(11a-11b\right) \\ \mathrm{This}\mathrm{is}\mathrm{not}\mathrm{equal}\mathrm{to}\left(-a-7b\right). \\ \mathrm{Thus},\mathrm{the}\mathrm{L}.\mathrm{H}.\mathrm{S}.\mathrm{is}\mathrm{not}\mathrm{equal}\mathrm{to}\mathrm{the}\mathrm{R}.\mathrm{H}.\mathrm{S}. \end{gathered}$$

(iv) T

$$\begin{gathered} \frac{-8}{7}{x}^3{y}^4 \\ \mathrm{Given}: \\ x=2 \\ y=1 \\ \mathrm{Given}\mathrm{expression}=\frac{-8}{7}{\left(2\right)}^3{\left(1\right)}^4 \\ =\frac{-8}{7}\times 8\times 1 \\ =\frac{-64}{7} \end{gathered}$$

(v) T

$$\begin{gathered} \frac{x}{4}+\frac{x}{6}-\frac{x}{2}=\frac{3}{4} \\ \Rightarrow \frac{3x+2x-6x}{12}=\frac{3}{4} \\ \Rightarrow \frac{-x}{12}=\frac{3}{4} \\ \Rightarrow -4x=36 \\ \Rightarrow x=-\frac{36}{4} \\ \Rightarrow x=-9 \end{gathered}$$

(vi) F

$$\begin{gathered} 2x-5=0 \\ \Rightarrow 2x=5 \\ \Rightarrow x=\frac{5}{2} \end{gathered}$$