Question

find x
$\bf\frac{x + 4}{2x + 1} = \frac{x + 2}{2x - 1}$
​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

${\large{\pmb{\sf{\underline{\underline{\maltese{ \: Question...}}}}}}}$

$\dashrightarrow{\sf{\dfrac{x + 4}{2x + 1} = \dfrac{x + 2}{2x - 1}}}$

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

${\large{\pmb{\sf{\underline{\underline{\maltese{ \: Solution...}}}}}}}$

$: \small{\pmb{ \implies}}{\sf{\dfrac{x + 4}{2x + 1} = \dfrac{x + 2}{2x - 1}}}$

• By cross multiplication

${: {\pmb{ \implies}}{\sf {\bigg(x (2x - 1) \bigg) + \bigg({4 (2x - 1) \bigg)}}= \bf \bigg({x (2x + 1)} \bigg) + \bigg(2(2x + 1)\bigg)}}$

${: {\pmb{ \implies}}{\sf {\bigg(2 {x}^{2} - x \bigg) + \bigg({8 {x} - 4 \bigg)}}= \bf \bigg({2 {x}^{2} + x} \bigg) + \bigg(4x+ 2\bigg)}}$

• Canceling (2x²) from both side

${: {\pmb{ \implies}}{\sf{\bigg({\cancel{2 {x}^{2}} - x} \bigg) + \bigg({8x - 4 \bigg)}}= \bf \bigg({\cancel{2 {x}^{2}} + x} \bigg) + \bigg(4x+ 2\bigg)}}$

${: {\pmb{ \implies}}{\sf{\bigg({- x} + {8x\bigg) - 4 }}= \bf \bigg({ + x} +4x\bigg)+ 2}}$

${: {\pmb{ \implies}}{\sf{\bigg({7x\bigg) - 4 }}= \bf \bigg(5x\bigg)+ 2}}$

${: {\pmb{ \implies}}{\sf{{7x - 5x}}= \bf 4+ 2}}$

${: {\pmb{ \implies}}{\sf{{2x}}= \bf 6}}$

${: {\pmb{ \implies}}{\sf{{x}}= \bf \dfrac{6}{2}}}$

${: {\pmb{ \implies}}{\sf{{x}}= \bf \cancel\dfrac{6}{2}}}$

${: {\pmb{ \implies}}{\sf{{x}}= \bf 3}}$

$\quad\bigstar{\underline{\boxed{\pmb{\sf{\red{x= \bf 3}}}}}}$

• The value of x is 3.

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

${\large{\pmb{\sf{\underline{\underline{\maltese{ \: Verification...}}}}}}}$

$: {\pmb{ \implies}}{\sf{\dfrac{x + 4}{2x + 1} = \dfrac{x + 2}{2x - 1}}}$

• Substituting the values of x = 3

$: {\pmb{ \implies}}{\sf{\dfrac{3 + 4}{(2 \times 3) + 1} = \dfrac{3 + 2}{(2 \times 3) - 1}}}$

$: {\pmb{ \implies}}{\sf{\dfrac{7}{(6) + 1} = \dfrac{5}{(6) - 1}}}$

$: {\pmb{ \implies}}{\sf{\dfrac{7}{7} = \dfrac{5}{5}}}$

$: {\pmb{ \implies}}{\sf{{\cancel\dfrac{7}{7}} = {\cancel\dfrac{5}{5}}}}$

$: {\pmb{ \implies}}{\sf{1 = 1}}$

$\quad\bigstar{\underline{\boxed{\pmb{\sf{\red{LHS=RHS}}}}}}$

• Hence Verified!

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

${\large{\pmb{\sf{\underline{\underline{\maltese{ \: Learn \: More...}}}}}}}$

• $\leadsto$ + = plus sign
• $\leadsto$ - = minus sign
• $\leadsto$ ± = plus - minus
• $\leadsto$ ∓ = minus - plus
• $\leadsto$ ( ) = parentheses
• $\leadsto$ [ ] = brackets
• $\leadsto$ (=) equals sign