Question

CLASS:-7

( MATHS )

CH-7
LINEAR EQUATION IN ONE VARIABLE...


Please answer the above attachment....✍️


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Answer 1

1. Let's solve your equation step-by-step.

0.5x - (0.8 - 0.2x) = 0.2 - 0.3x

Step 1: Simplify the equation.

⇒ 0.5x - (0.8 - 0.2x) = 0.2 - 0.3x

⇒ 0.5x - 0.8 + 0.2x = 0.2 - 0.3x

Step 2: Combine Like Terms

⇒ 0.5x - 0.8 + 0.2x = 0.2 - 0.3x

⇒ 0.5x + 0.2x - 0.8 = 0.2 - 0.3x

⇒ 0.7x - 0.8 = 0.2 - 0.3x

Step 3: Add 0.3x to both sides of the equation.

⇒ 0.7x - 0.8 + 0.3x = 0.2 - 0.3x + 0.3x

⇒ 0.7x + 0.3x - 0.8 = 0.2

⇒ 1x - 0.8 = 0.2

Step 4: Add 0.8 to both sides of the equation.

⇒ x - 0.8 + 0.8 = 0.2 + 0.8

⇒ x = 1

∴ x = 1 in the equation → 0.5x - (0.8 - 0.2x) = 0.2 - 0.3x

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2. Let's solve your equation step-by-step.

$0.5x +\dfrac{x}{3} =0.25x+7$

Step 1: Simplify the equation.

⇒ $0.5x +\dfrac{x}{3} =0.25x+7$

⇒ $\dfrac{5}{10} x +\dfrac{1}{3}x =0.25x+7$

⇒ $\dfrac{5\times 3 }{10\times 3 } x +\dfrac{1\times 10 }{3\times 10}x =0.25x+7$

⇒ $\dfrac{15 }{30 } x +\dfrac{10 }{30}x =0.25x+7$

⇒ $\dfrac{25 }{30 } x =0.25x+7$

Step 2: Subtract 0.25x from both sides of the equation.

⇒ $\dfrac{25 }{30 } x -0.25x =0.25x+7 - 0.25x$

⇒ $\dfrac{25 }{30 } x -\dfrac{25}{100} x =7$

⇒ $\dfrac{25\times 10 }{30\times 10 } x -\dfrac{25\times 3 }{100\times 3 } x =7$

⇒ $\dfrac{250 }{300 } x -\dfrac{75}{300 } x =7$

⇒ $\dfrac{175}{300}x =7$

Step 3: Multiply $\frac{300}{175}$ to both sides of the equation.

⇒ $x = 7\times \dfrac{300}{175}$

⇒ $x = \dfrac{300}{25}$

⇒ $x = 12$

∴ x = 12 in the equation → $\bf 0.5x +\dfrac{x}{3} =0.25x+7$

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Answer 2

$31)\:\:\bf\blue{0.5\:x\:-\:(0.8\:-\:0.2\:x)\:=\:0.2\:-\:0.3\:x}$

❶ First we remove the bracket & multiple with -ve sign.

$:\implies\:\:\bf{0.5\:x\:-\:0.8\:+\:0.2\:x\:=\:0.2\:-\:0.3\:x}$

❷ Now put all x co-efficient numbers to one side and all real numbers to other side with sign.

$:\implies\:\:\bf{0.5\:x\:+\:0.2\:x\:+\:0.3\:x\:=\:0.2\:+\:0.8}$

❸ Now adding the above we get,

$:\implies\:\:\bf{1.0\:x\:=\:1.0}$

❹ Now take 1 to R.H.S & divide with 1.

$:\implies\:\:\bf{x\:=\:\dfrac{1}{1}}$

❺ Finally we get,

$:\implies\:\:{\underline{\boxed{\bf{\orange{x\:=\:1}}}}}$

━─━─━─━─━─━─━─━─━─━─━─━─━─━─━

32》$\bf\purple{0.5\:x\:+\:\dfrac{x}{3}\:=\:0.25\:x\:+\:7}$

❶ First we add L.H.S with taking L.C.M.

$:\implies\:\:\bf{\dfrac{1.5\:x\:+\:x}{3}\:=\:0.25\:x\:+\:7}$

❷ Multiple 3 (denominator) in R.H.S.

$:\implies\:\:\bf{2.5\:x\:=\:0.75\:x\:+\:21}$

❸ Take 0.75x in L.H.S & subtract it with 2.5x.

$:\implies\:\:\bf{2.5\:x\:-\:0.75\:x\:=\:21}$

$:\implies\:\:\bf{1.75\:x\:=\:21}$

❹ Now take 1.75 to R.H.S & divide with 21.

$:\implies\:\:\bf{x\:=\:\dfrac{21}{1.75}}$

$:\implies\:\:\bf{x\:=\:\dfrac{2100}{175}}$

❺ Finally we get,

$:\implies\:\:{\underline{\boxed{\bf{\green{x\:=\:12}}}}}$