Exercise 7A
Q1 |Ex-7A | Class 7 | Linear Equation with one Variable | S.Chand |Composite Mathematics |Chapter 7 |myhelper
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: $P=\frac{4}{7}+\frac{2}{7}$
$P=\frac{6}{7}$
Q2 |Ex-7A | Class 7 | Linear Equation with one Variable | S.Chand |Composite Mathematics |Chapter 7 |myhelper
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: $g=10 \times 2.9$
$g=29 Ans$
Q3 |Ex-7A | Class 7 | Linear Equation with one Variable | S.Chand |Composite Mathematics |Chapter 7 |myhelper
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: $m=5 \times 6=30$
Q4 |Ex-7A | Class 7 | Linear Equation with one Variable | S.Chand |Composite Mathematics |Chapter 7 |myhelper
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
Q5 |Ex-7A | Class 7 | Linear Equation with one Variable | S.Chand |Composite Mathematics |Chapter 7 |myhelper
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: $\Rightarrow 12-x=5 x$
$\Rightarrow 12=54+x$
$\Rightarrow 12=64$
$\Rightarrow x=\frac{12}{6}$
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