Question

linear equation process + check also please I'll mark as brainliest please​

Answer 1

Answer:

Step 1: Simplify each side, if needed.

Step 2: Use Add./Sub. Properties to move the variable term to one side and all other terms to the other side.

Step 3: Use Mult./Div. ...

Step 4: Check your answer.

I find this is the quickest and easiest way to approach linear equations.

Example 6: Solve for the variable.

Answer 2

Answer:

Answer :

The value of is 23/8.

$\begin{gathered}\end{gathered}$

Question :

${\implies{\sf{ \: \: \dfrac{3}{4}(2x - 5) - \dfrac{5}{6} (7 - 5x)= \dfrac{7x}{3}}}}$

Solution :

${\implies{\sf{ \: \: \dfrac{3}{4}(2x - 5) - \dfrac{5}{6} (7 - 5x)= \dfrac{7x}{3}}}}$

${\implies{\sf{ \: \: \dfrac{3(2x - 5)}{4} - \dfrac{5 (7 - 5x)}{6}= \dfrac{7x}{3}}}}$

${\implies{\sf{ \: \: \dfrac{6x - 15}{4} - \dfrac{35 - 25x}{6}= \dfrac{7x}{3}}}}$

${\implies{\sf{ \: \: \dfrac{3(6x - 15) - 2(35 - 25x)}{12}= \dfrac{7x}{3}}}}$

${\implies{\sf{ \: \: \dfrac{18x - 45 - 70 - 50x}{12}= \dfrac{7x}{3}}}}$

${\implies{\sf{ \: \: \dfrac{18x - 115 - 50x}{12}= \dfrac{7x}{3}}}}$

${\implies{\sf{ \: \: \dfrac{18x - 115 + 50x}{12}= \dfrac{7x}{3}}}}$

${\implies{\sf{ \: \: \dfrac{68x - 115}{12}= \dfrac{7x}{3}}}}$

${\implies{\sf{ \: \: {68x - 115}= \dfrac{7x}{3} \times 12}}}$

${\implies{\sf{ \: \: {68x - 115}= \dfrac{7x}{\cancel{3}} \times \cancel{12}}}}$

${\implies{\sf{ \: \: {68x - 115}= {7x \times 4}}}}$

${\implies{\sf{ \: \: {68x - 115}= 28x}}}$

${\implies{\sf{ \: \: {68x - 28x = 115}}}}$

${\implies{\sf{ \: \: {40x = 115}}}}$

${\implies{\sf{ \: \: {x = \dfrac{115}{40}}}}}$

${\implies{\sf{ \: \: {x = \cancel{\dfrac{115}{40}}}}}}$

${\implies{\sf{ \: \:{\underline{\underline{\red{x = \dfrac{23}{8}}}}}}}}$

Hence, the value of x is 23/8.

$\begin{gathered}\end{gathered}$

Checking :

${\implies{\sf{ \: \: \dfrac{3}{4}(2x - 5) - \dfrac{5}{6} (7 - 5x)= \dfrac{7x}{3}}}}$

Substituting the value of x = 23/8

${\implies{\sf{ \: \: \dfrac{3}{4} \bigg(2 \times \dfrac{23}{8} - 5 \bigg) - \dfrac{5}{6} \bigg(7 - 5 \times \dfrac{23}{8} \bigg)= \dfrac{7}{3} \times \dfrac{23}{8} }}}$

${\implies{\sf{ \: \: \dfrac{3}{4} \bigg(\dfrac{2 \times 23}{8} - 5 \bigg) - \dfrac{5}{6} \bigg(7 - \dfrac{5 \times 23}{8} \bigg)= \dfrac{7 \times 23}{24}}}}$

${\implies{\sf{ \: \: \dfrac{3}{4} \bigg(\dfrac{46}{8} - 5 \bigg) - \dfrac{5}{6} \bigg(7 - \dfrac{115}{8} \bigg)= \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: \dfrac{3}{4} \bigg(\dfrac{46 - 40}{8} \bigg)- \dfrac{5}{6} \bigg(\dfrac{56 - 115}{8} \bigg)= \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: \dfrac{3}{4} \bigg(\dfrac{6}{8} \bigg)- \dfrac{5}{6} \bigg(\dfrac{ - 59}{8} \bigg)= \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: \bigg( \dfrac{3}{4} \times \dfrac{6}{8} \bigg)- \bigg(\dfrac{5}{6} \times \dfrac{ - 59}{8} \bigg)= \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: \bigg( \dfrac{3 \times 6}{4 \times 8} \bigg)- \bigg(\dfrac{ 5 \times - 59}{6 \times 8} \bigg)= \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: \bigg( \dfrac{18}{32} \bigg)- \bigg(\dfrac{ - 295}{48} \bigg)= \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: \dfrac{18}{32} - \dfrac{ - 295}{48} = \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: \dfrac{(18 \times 3) - ( - 295 \times 2)}{96} = \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: \dfrac{(54) - ( - 590)}{96} = \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: \dfrac{54 + 590}{96} = \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: \dfrac{644}{96} = \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: \cancel{\dfrac{644}{96}} = \dfrac{161}{24}}}}$

${\implies{\sf{ \: \: { \dfrac{161}{24} } = \dfrac{161}{24}}}}$

${\implies{\sf{ \: \:{\underline{\underline{\red{LHS = RHS}}}}}}}$

Hence Verified!

$\begin{gathered}\end{gathered}$

Learn More :

✧ Algebraic identities:-

⠀⇢ (a+b)²+(a-b)² = 2a²+2b²

⠀⇢ (a+b)²-(a-b)² = 4ab

⠀⇢ (a+b)(a -b) = a²-b²

⠀⇢ (a+b+c)² = a²+b²+c²+2ab+2bc+2ca

⠀⇢ (a-b)³ = a³-b³-3ab(a-b)

⠀⇢ (a³+b³) = (a+b)(a²-ab+b²)

⠀⇢ a²+b² = (a+b)²-2ab

⠀⇢ a³-b³ = (a-b)(a²+ab +b²)

⠀⇢ If a + b + c = 0 then a³ + b³ + c³ = 3abc

✧ BODMAS :

↝ BODMAS rule is an acronym used to remember the order of operations to be followed while solving expressions in mathematics.

It stands for :-

⠀ »» B - Brackets,

⠀ »» O - Order of powers or roots,

⠀ »» D - Division,

⠀ »» M - Multiplication 

⠀ »» A - Addition

⠀ »» S - Subtraction.

↝ It means that expressions having multiple operators need to be simplified from left to right in this order only.

✧ BODMAS RULE :

↝ First, we solve brackets, then powers or roots,then division or multiplication (whatever comes first from the left side of the expression), and then at last subtraction or addition.

⠀ ↠ Addition (+)

⠀ ↠ Subtraction (-)

⠀ ↠ Multiplication (×)

⠀ ↠ Division (÷)

⠀ ↠ Brackets ( )

$\underline{\rule{220pt}{4pt}}$