Question

Match the following columns please
Urgent

Answer 1

$\sf\:AnswerS:$

$\tt\:(a) \:7$ ⠀ ⠀⠀ ↠⠀ ⠀ $\tt\color{teal}{(iv)}$

$\tt\:(b) \:-5$ ⠀ ⠀ ↠⠀ ⠀ $\tt\color{teal}{(i)}$

$\tt\:(c) \:\frac{31}{6}$ ⠀ ⠀ ⠀↠⠀ ⠀ $\tt\color{teal}{(ii)}$

$\tt\:(d) \:4$ ⠀ ⠀⠀ ↠⠀ ⠀ $\tt\color{teal}{(iii)}$

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$\bf\:Step~wise~Calculation$

Question 1 :

$\tt\:\frac{x}{5}=\frac{x-1}{6}$

Cross multiplying

$\tt\implies\:6x=5(x-1)$

Multiplying and removing the brackets

$\tt\implies\:6x=5x-5$

Transposing +5x from RHS to LHS it becomes -5x

$\tt\implies\:6x-5x=-5$

$\tt\color{navy}{\implies\:x=-5}$

‎________________

Question 2 :

$\tt\:\frac{0.2x+5}{3.5x-3}=\frac{2}{5}$

Cross multiplying

$\tt\implies\:2(3.5x-3) =5(0.2x+5)$

Multiplying and removing the brackets

$\tt\implies\:7x-6=x+25$

Transposing x from RHS to LHS it becomes -x

$\tt\implies\:7x-x-6=25$

$\tt\implies\:6x-6=25$

Transposing -6 from LHS to RHS it becomes +6

$\tt\implies\:6x=25+6$

$\tt\implies\:6x=31$

Transposing 6 to RHS it goes to the denominator

$\tt\color{navy}{\implies\:x=\frac{31}{6}}$

________________

Question 3 :

$\tt\:8x-7-3x=6x-2x-3$

Arranging the terms

$\tt\implies\:8x-3x-7=6x-2x-3$

Proceeding the calculations on like terms

$\tt\implies\:5x-7=4x-3$

Transposing +4x from RHS to LHS it becomes -4x

$\tt\implies\:5x-4x-7=-3$

$\tt\implies\:x-7=-3$

Transposing -7 from LHS to RHS it becomes +7

$\tt\implies\:x=-3+7$

$\tt\color{navy}{\implies\:x=4}$

________________

Question 4 :

$\tt\:5(x-1) -2(x+8) =0$

Multiplying and removing the brackets

$\tt\implies\:5x-5 -2x-16 =0$

Arranging the terms and proceeding with the calculations

$\tt\implies\:5x-2x-5-16 =0$

$\tt\implies\:3x-5-16 =0$

$\tt\implies\:3x-21 =0$

Transposing -21 from LHS to RHS it becomes +21

$\tt\implies\:3x=21$

Transposing 3 to RHS it goes to the denominator

$\tt\implies\:x=\frac{21}{3}$

Reducing the fraction to the lower terms

$\tt\implies\:x=\cancel{\frac{21}{3}}$

$\tt\color{navy}{\implies\:x=7}$

________________

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