SChand Composite Mathematics Class 7 Chapter 7 Linear Equation with one Variable Exercise 7A

 Exercise 7A 

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Q1 |Ex-7A | Class 7 | Linear Equation with one Variable | S.Chand |Composite Mathematics |Chapter 7 |myhelper

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Question 1

Solve the following equations by transposition : 

(i) x+5=9

Sol: x=9-5=4

(ii) a+10=12

Sol: a= 12 -10=2

(iii)  $x+\frac{3}{5}=\frac{4}{5}$

Sol: $\Rightarrow x=\frac{4}{5}-\frac{3}{5}$

$\Rightarrow x=\frac{4-3}{5}=\frac{1}{5}$

(iv) n+1.8=3

Sol: $n=3-1.8$ 

n=1.2

(v)  x-7=4

Sol: $\Rightarrow 2=4+7=11$

(vi)  $x-4.2=11.4$

Sol: $x=11.4+4.2$

$x=15.6$

(vii)  $-12+a=23$

Sol: $a=23+12=35$

(viii)  $P-\frac{2}{7}=\frac{4}{7}$

Sol:  $P=\frac{4}{7}+\frac{2}{7}$

$P=\frac{6}{7}$

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Q2 |Ex-7A | Class 7 | Linear Equation with one Variable | S.Chand |Composite Mathematics |Chapter 7 |myhelper

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Question 2

Solve each equation: 

(i) 3y=9

Sol: $y=\frac{9}{3}=3$ 

(ii) 7y=75

Sol: $y=\frac{75}{5}=15$

(iii) -7a =84 

Sol: $a=\frac{84}{-7}=-12$

(iv) $-8 m=-24$

Sol: $m=\frac{-24}{-8}=3$ 

(v) $\frac{j}{7}=5$

Sol: $j=7 \times 5=35$

(vi) $\frac{x}{2}=-10$ 

Sol: $x=-10 \times 2=-20$

(vii) $\frac{w}{-8}=-4$

Sol: w=$-4\times -8$

w=32

(viii) $\frac{g}{2.9}=10$ 

Sol: $g=10 \times 2.9$

$g=29 Ans$

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Q3 |Ex-7A | Class 7 | Linear Equation with one Variable | S.Chand |Composite Mathematics |Chapter 7 |myhelper

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Question 3

Write the following statements in equation form. Find numerals to make true statements.

(i) The sum of 5 and x is 12 

Ans: equation form = 5 +x =12 

Sol: 7

(ii) x decreased by 7 is 13

Ans: equation form= x-7=13 

Sol: 20

(iii) Six less than two times $y$ is 32

Ans: equation form= $2 y-6=32$ 

Sol: $2 y=38 ; y=19$

(iv)  If 8 is taken away from the number $n$, the result is $-4$

Ans: equation form= $n-8=-4$ 

Sol: n=4

(v) 9 multiplied by r is 36 

Ans: equation form =$9 \times r=36$

Sol: r=4

(vi)  q multiplied by 7 gives-35 

Ans: $9 \times 7=-35$ 

Sol: q=-35

(vii) If d is divided by -4 the result is 3 

Ans: $d \div-4=3$

Sol: $d=-4 \times 3=-12$ 

(viii) Eight decreased by 3 times a number equals 2.

Sol :

Equation : 8-3x=2

-3x=2-8

-3x=-6

$x=\frac{-6}{-3}=2$

x=2

(ix) The product of 7 and the number x is 42

Ans: $7 \times x=42$

Sol: x=6 

(x) Quotient of m divided by 5 is 6. 

Ans: $\frac{m}{5}=6$ 

Sol: $m=5 \times 6=30$

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Q4 |Ex-7A | Class 7 | Linear Equation with one Variable | S.Chand |Composite Mathematics |Chapter 7 |myhelper

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Question 4

Solve the following equation: 

(i) $5 x+2=3 x+12$ 

Sol: $5 x-3 x=12-2$ 

= $2 x=10 \Rightarrow x=\frac{10}{2}=5$

(ii) $6 y-9=2 y+15$

Sol: $6 y-2 y=15+9$

=$4 y=24$

$y=\frac{24}{4} \quad \Rightarrow \quad y=6$

(iii) $2 x-3=9-x$

Sol: $\Rightarrow 2x+x=9+3$

$\Rightarrow \quad 3x=12$

$\Rightarrow \quad x=\frac{12}{3}$

$x=4$ 

(iv)  $2 a-5=8 a+1$ 

Sol: $2 a-8 a=5+1$

$\begin{aligned}-6 a &=6 \\ a &=\frac{6}{-6} \\ a &=-1 \end{aligned}$

(v) b+3=33-b

Sol: $b+b=33-3$

$\begin{aligned} 2 b &=30 \\ b &=\frac{30}{2} \\ b &=15 \end{aligned}$

(vi) 1.9x+3.6 =2.5x+3

Sol: 1.9x-2.5x = 3-3.5

 $\begin{aligned}-0.6 x &=-0.6 \\ x &=-\frac{0.6}{0.6} \end{aligned}$

x=1

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Q5 |Ex-7A | Class 7 | Linear Equation with one Variable | S.Chand |Composite Mathematics |Chapter 7 |myhelper

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Question 5

Solve the following equations 

(i) $6 x+14=16$

Sol: $\Rightarrow 6 x=16-14$

$\Rightarrow 6 x=2$

$\Rightarrow \quad x=\frac{2}{6}$

$\Rightarrow \quad x=\frac{1}{3}$

(ii) $7+5 x-3 x=21$

Sol: $2x=21-7$

$2x=14$

$x=\frac{14}{2}$

$x=7$

(iii) $1.2 x+4.8x=18$

Sol: $6 x=18$

$x=\frac{18}{6}=3$

(iv) $6(5 x-2)+12=30$

Sol: $30 x-12+12=30$

$30 x=30$

$x=\frac{30}{30}=1$

(v) $7(x-4)+13=6$

Sol: $\Rightarrow 7 x-28+13=6$

$\Rightarrow 7 x-15=6$

$\Rightarrow 7 x=6+15$

$\Rightarrow \quad x=\frac{21}{7}=3$

(vi) $5(6 x+1)=3(-8+x)+2$

Sol: $30 x+5=-24+3 x+2$ 

$\Rightarrow 30 x-3 x=-24+2-5$

$\Rightarrow 27 x=-27$

$\Rightarrow \quad x=\frac{-27}{27}=-1$

(vii) $4-4(x-5)=2(2-x)-6$

Sol: $\Rightarrow 4-4 x+20=4-2 x-6$

$\Rightarrow-4 x+2 x=4-6-4-20$

$\Rightarrow-2 x=-26$

$\Rightarrow-2 x=-26 \Rightarrow x=-\frac{26}{-2} \Rightarrow x=13$

(viii) $10 y-0.2(7-y)=19$

Sol:$\Rightarrow 10 y-1.4+0.2 y=19$

$\Rightarrow 10.2 y=19+1.4$

$\Rightarrow y=\frac{20.4}{10.2}$

$\Rightarrow y=2$

(ix) $\frac{12-x}{5}=x$

Sol: $\Rightarrow 12-x=5 x$

$\Rightarrow 12=54+x$

$\Rightarrow 12=64$

$\Rightarrow x=\frac{12}{6}$