EXERCISE 15 A
Solve the following equations:
Q1 | Ex-15A | Class 8 | S.Chand | Composite maths | chapter 15 |Linear Equations | myhelper
Question 1
3(x+1) + 4x = 24
Sol :
⇒ 3x+3+4x=24
⇒ 7x=24-3
⇒ 7x=21
⇒ $x=\dfrac{21}{7}$
⇒ $x=3$
Question 2
16-2(3y+5) = 4(y-2)
Sol:
⇒16-6y-10=4y-8
⇒16-10+8=4y+6y
⇒24-10=10y
⇒14=10y
⇒$y=\dfrac{14}{10}$
⇒y=1.4
Question 3
3(z+1)+4(z+0.3) = 20z + 0.95
Sol:
⇒3z+3+4z+1.2=20z+0.95
⇒7z+4.2=20z+0.95
⇒4.2-0.95=20z-7z
⇒3.25=13z
⇒$z=\dfrac{3.25}{13}$
⇒z=0.25
Question 4
7m-4(m+6) = 7(m-8)+4
Sol :
⇒7m-4m-24=7m-56+4
⇒3m-24=7m-52
⇒52-24=7m-3m
⇒28=4m
⇒$m=\dfrac{28}{4}$
⇒m=7
Question 5
$\dfrac{x}{2}+\dfrac{x}{3} = 15$
Sol :
Take L.C.M of 2 and 3 = 6
⇒$\dfrac{x\times 3 + x\times 2}{6}=15$
⇒$\dfrac{3x+2x}{6}=15$
⇒$\dfrac{5x}{6}=15$
⇒$x=\dfrac{15\times 6}{5}$
⇒x=18
Question 6
$\dfrac{4(x+2)}{5}=7+\dfrac{5x}{13}$
Sol :
⇒$\dfrac{4x+8)}{5}=7+\dfrac{5x}{13}$
⇒$\dfrac{4x+8}{5}=\dfrac{7\times 13+5x}{13}$
⇒$\dfrac{4x+8}{5}=\dfrac{91+5x}{13}$
⇒13(4x+8)=5(91+5x)
⇒52x+104=455+25x
⇒52x-25x=455-104
⇒27x=351
⇒$x=\dfrac{351}{27}$
⇒x=13
Question 7
$\dfrac{x+3}{2}-\dfrac{4}{3}=\dfrac{3x-7}{3}$
Sol :
L.C.M of 2 and 3 is 6
⇒$\dfrac{3(x+3)-2(4)}{6}=\dfrac{3x-7}{3}$
⇒$\dfrac{3x+9-8}{6}=\dfrac{3x-7}{3}$
⇒$\dfrac{3x+1}{6}=\dfrac{3x-7}{3}$
⇒3(3x+1)=6(3x-7)
⇒9x+3=18x-42
⇒42+3=18x-9x
⇒9x=45
⇒$x=\dfrac{45}{9}$
⇒x=5
Question 8
$\dfrac{5x+1}{2}-\dfrac{x-2}{6}=\dfrac{2x+4}{3}$
Sol :
L.C.M of 2 and 6 is 6
⇒$\dfrac{3(5x+1)-(x-2)}{6}=\dfrac{2x+4}{3}$
⇒$\dfrac{15x+3-x+2}{6}=\dfrac{2x+4}{3}$
⇒$\dfrac{14x+5}{6}=\dfrac{2x+4}{3}$
⇒3(14x+5)=6(2x+4)
⇒42x+15=12x+24
⇒42x-12x=24-15
⇒30x=9
⇒$x=\dfrac{9}{30}$
⇒$x=\dfrac{3}{10}$
Question 9
$\dfrac{9x-5}{7}=\dfrac{6x+2}{5}$
Sol :
⇒5(9x-5)=7(6x+2)
⇒45x-25=42x+14
⇒45x-42x=14+25
⇒3x=39
⇒$x=\dfrac{39}{3}$
⇒x=13
Question 10
$\dfrac{9x}{7-6x}=2$
Sol :
⇒2(7-6x)=9x
⇒14-12x=9x
⇒14=9x+12x
⇒14=21x
⇒$x=\dfrac{14}{21}$
⇒$x=\dfrac{2}{3}$
Question 11
$\dfrac{2x-1}{3x+1}=\dfrac{6x-1}{9x-3}$
Sol:
⇒(2x-1)(9x-3)=(6x-1)(3x+1)
⇒$2 x(9 x-3)-1(9 x-3)=6 x(3 x+1)-(3 x+1)$
$\Rightarrow 18 x^{2}-6 x-9 x+3=18 x^{2}+6 x-3 x-1$
$\Rightarrow 18 x^{2}-15 x+3=18 x^{2}+3 x-1$
$\Rightarrow 18 x^{2}-18 x^{2}-15 x-3 x=-1-3$
$\Rightarrow-18 x=-4$
$\Rightarrow x=\frac{-4}{-18}=\frac{2}{9}$
Question 12
$\dfrac{(1-3y)(4-y)}{(2-3y)(1-y)}=1$
Sol :
⇒(1-3y)(4-y)=(2-3y)(1-y)
⇒1(4-y)-3y(4-y)=2(1-y)-3y(1-y)
⇒$4-y-12 y+3 y^{2}=2-2 y-3 y+3 y^{2}$
⇒y-13y=2-5y
⇒2=8y
⇒$y=\frac{2}{8}$
Question 13
$\dfrac{(4x+4)-(7x-8)}{4x+5}=-\dfrac{4}{3}$
Sol :
⇒$\dfrac{4x+4-7x+8}{4x+5}=-\dfrac{4}{3}$
⇒$\dfrac{-3x+12}{4x+5}=-\dfrac{4}{3}$
⇒3(-3x+12)=-4(4x+5)
⇒-9x+36=-16x-20
⇒16x-9x=-20-36
⇒7x=-56
⇒x=-8
It is correct but solution are not full
ReplyDeleteJitna Mila utne me khush reh sakee chapne ke liye ate aur bolte pura nahi hai answer
DeleteThanks a lot for your help
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