Question
Solve the following equations. Check your result in case.
2(x - 2) + 3(4x - 1) = 0
2(x - 2) + 3(4x - 1) = 0
✓
Answer
2(x - 2) + 3(4x - 1) = 0
⇒ 2x - 4 + 12x - 3 = 0
⇒ 2x + 12x = 4 + 3 (By transposing)
⇒ 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 $\text{x}=\frac{1}{2}$
⇒ 2x - 4 + 12x - 3 = 0
⇒ 2x + 12x = 4 + 3 (By transposing)
⇒ 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
The area of a square plot is $6084 m^2$. Find the length of the wire which can go four times along the boundary of the plot.
→As shown in the figure, four napkins all of the same size were made from a square piece of cloth of length 1 m. What length of lace will be required to trim all four sides of all the napkins ?
Find the interest on Rs. 500 for a period of 4 years at the rate of 8% per annum. Also, find the amount to be paid at the end of the period.
A group of 120 men had provisions for 200 days. After 5 days, 30 men died due to an epidemic. How long will the remaining food last?
Discuss the characteristics of various groups of numbers in class and complete the table below. In front of each group, write the inference you make after carrying out the operations of addition, subtraction, multiplication and division, using a (✓) or a (x).
Remember that you cannot divide by zero.
Remember that you cannot divide by zero.
| Group of Numbers | Addition | Subtraction | Multiplication | Division |
| Natural Numbers | ✓ | X (7- 10 =-3) | ✓ | \begin{gathered} x \\ (3 \div 5= \left.\frac{3}{5}\right) \end{gathered} |
| Integers | ||||
| Rational Numbers |
Complete the table given below.
→| $-3$ | $\frac{3}{5}$ | $-17$ | $\frac{-5}{11}$ | $5$ | |
| Natural Numbers | $x$ | $\checkmark$ | |||
| Integers | $\checkmark$ | ||||
| Rational Numbers | $\checkmark$ |
Simplify:
$8-4\frac{1}{2}-2\frac{4}{1}=\frac{8}{1}-\frac{9}{2}-\frac{9}{4}$
→$8-4\frac{1}{2}-2\frac{4}{1}=\frac{8}{1}-\frac{9}{2}-\frac{9}{4}$
virat made twice as many runs as Rohit. The total of their scores is 2 less than a double century. How many runs did each of them make ?
Simplify:
$2+\frac{-1}{2}+\frac{-3}{4}$
→$2+\frac{-1}{2}+\frac{-3}{4}$
Solve the following equations. Check your result in case.
0.5x - (0.8 - 0.2x) = 0.2 - 0.3x
0.5x - (0.8 - 0.2x) = 0.2 - 0.3x