Question
Solve the following equations. Check your result in case.
$\frac{2\text{x}+5}{3\text{x}+4}=3$
$\frac{2\text{x}+5}{3\text{x}+4}=3$
✓
Answer
$\frac{2\text{x}+5}{3\text{x}+4}=3$
(By cross multiplication)
$3(3\text{x}+4)=1(2\text{x}+5)$
$9\text{x}+12=2\text{x}+5$
$\Rightarrow9\text{x}-2\text{x}=5-12$
$\Rightarrow7\text{x}=-7$
$\Rightarrow\text{x}=\frac{-7}{7}=-1$
$\text{x}=-1$
Check:
$\text{L.H.S}.=\frac{2\text{x}+5}{3\text{x}+4}=\frac{2(-1)+5}{3(-1)+4}=\frac{-2\ +\ 5}{-3\ +\ 4}$
$=\frac{3}{1}=3=\text{R.H.S.}$
Hence $\text{x}=-1$
(By cross multiplication)
$3(3\text{x}+4)=1(2\text{x}+5)$
$9\text{x}+12=2\text{x}+5$
$\Rightarrow9\text{x}-2\text{x}=5-12$
$\Rightarrow7\text{x}=-7$
$\Rightarrow\text{x}=\frac{-7}{7}=-1$
$\text{x}=-1$
Check:
$\text{L.H.S}.=\frac{2\text{x}+5}{3\text{x}+4}=\frac{2(-1)+5}{3(-1)+4}=\frac{-2\ +\ 5}{-3\ +\ 4}$
$=\frac{3}{1}=3=\text{R.H.S.}$
Hence $\text{x}=-1$
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
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 |
Mangoes are sold at $\text{Rs. }43\frac{1}{2}\text{per kg.}$ What is the weight of mangoes available for $\text{Rs. }326\frac{1}{4}?$
→Lines PQ and RS intersect at point M. m∠PMR = x°.What are the measures of ∠PMS, ∠SMQ and ∠QMR ?
Solve: $\frac{3\text{x}}{10}+\frac{2\text{x}}{5}=\frac{7\text{x}}{25}+\frac{29}{25}.$
→Find the sum:
$3\frac{4}{5}+2\frac{13}{10}+1\frac{1}{15}$
→$3\frac{4}{5}+2\frac{13}{10}+1\frac{1}{15}$
Evaluate:
$\frac{7}{24}-\frac{19}{36}$
→$\frac{7}{24}-\frac{19}{36}$
In the figure given alongside, find the measure of $\angle\text{ACD}.$
→The area of a rhombus is $441 cm^2$ and its height is 17.5 cm . Find the length of each side of the rhombus.
→What number must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3?
Simplify the following:
$a^2 b\left(a-b^2\right)+a b^2\left(4 a b-2 a^2\right)-a^3 b(1-2 b)$
→$a^2 b\left(a-b^2\right)+a b^2\left(4 a b-2 a^2\right)-a^3 b(1-2 b)$