Question
Solve the following equations. Check your result in case. $2(x - 2) + 3(4x - 1) = 0$
✓
Answer
$2(x - 2) + 3(4x - 1) = 0 $
$\Rightarrow 2x - 4 + 12x - 3 = 0 $
$\Rightarrow 2x + 12x = 4 + 3$ (By transposing)
$\Rightarrow 14x = 7$
$\Rightarrow\text{x}=\frac{7}{14}=\frac{1}{2}$
Check: $\text{L.H.S}=2(\text{x}-2)+3(4\text{x}-1)$
$=2\Big(\frac{1}{2}-2\Big)+3\Big(4\times\frac{1}{2}-1\Big)$
$=2\times\Big(\frac{1-4}{2}\Big)+3(2-1)$
$=2\text{x}\Big(\frac{-3}{2}\Big)+3(1)$
$=-3+3=0=\text{R.H.S.}$ Hence $\text{x}=\frac{1}{2}$
$\Rightarrow 2x - 4 + 12x - 3 = 0 $
$\Rightarrow 2x + 12x = 4 + 3$ (By transposing)
$\Rightarrow 14x = 7$
$\Rightarrow\text{x}=\frac{7}{14}=\frac{1}{2}$
Check: $\text{L.H.S}=2(\text{x}-2)+3(4\text{x}-1)$
$=2\Big(\frac{1}{2}-2\Big)+3\Big(4\times\frac{1}{2}-1\Big)$
$=2\times\Big(\frac{1-4}{2}\Big)+3(2-1)$
$=2\text{x}\Big(\frac{-3}{2}\Big)+3(1)$
$=-3+3=0=\text{R.H.S.}$ Hence $\text{x}=\frac{1}{2}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find five rational numbers between $\frac{-3}{5}\text{ and }\frac{-1}{2}$
→What happens to the value of the product, when we multiply two improper fractions?
→| $\frac{7}{3} \times \frac{5}{2}=\frac{35}{6}$ | $\frac{35}{6}>\frac{7}{3}, \frac{35}{6}>\frac{5}{2}$ | Product is greater than each of the fractions |
| $\frac{6}{5} \times \frac{\square}{3}=\frac{24}{15}$ | ||
| $\frac{9}{2} \times \frac{7}{\square}=\frac{63}{8}$ | ||
| $\frac{3}{\square} \times \frac{8}{7}=\frac{24}{14}$ |
The area of a square field is $\frac{1}{2}$ hectare. Find the length of its diagonal in metres. Hint: $1$ hectare = $10000m^2$.
→Simplify the following: $27-\Big[38-\big\{46-(15-\overline{13-2})\big\}\Big]$
→Each bag of cement weighs $48.5kg$. How many such bags will weigh $223\ kg$?
→The ratio of the radii of two circles is $3 : 2$. What is the ratio of their circumferences?
→Draw $\triangle\text{PQR}$ in which $\angle\text{Q}=80^\circ,$ $\angle\text{R}=55^\circ$ and $QR = 4.5\ cm$. Draw the perpendicular bisector of side $QR$.
→Find the gain or loss per cent when:
$CP = Rs. 2400$ and $SP = Rs. 2592$
→$CP = Rs. 2400$ and $SP = Rs. 2592$
In fig. (i) $\text{PL}\bot\text{OA}$ and $\text{PM}\bot\text{OB}$ such that $\text{PL}=\text{PM}$. Is $\triangle\text{PLO}\cong\triangle\text{PMO}?$ Give reason in support of your answer. 
→In Fig. two parallel lines $l$ and $m$ are cut by two transversals $p$ and $q.$ Determine the values of $x$ and $y.$ 
→