Question

solve the equations x+7/x+2=3/4​

Answer 1

$\underline \frak{ \pink{How\: To \: Do? }}$

Yep! it's easy:D

So here equation given-x+7/x+2=3/4, In this equation we have to find value of x or in other words we have to simplify this equation. For this first we have to do cross multiplication.To do cross multiplication, multiply 4 with x+7 and 3 with x+2.After multiplying the digits, add/subtract like terms i.e. 4x with 3x and 28 with 6.Then finally we will get owr Final answer i.e -22

Now Let's do it!

$\underline \frak{ \pink{Given \: Equation }}$

$\boxed{ \bf{ \dfrac{x + 7}{x + 2} = \dfrac{3}{4} }}$

Now Let's solve it:

$: \implies \sf{}\dfrac{x + 7}{x + 2} = \dfrac{3}{4}$

$: \implies \sf{}4(x + 7) = 3(x + 2)$

$: \implies \sf{}4x + 28 = 3x + 6$

$: \implies \sf{} - 6 + 28 = - 4x + 3x$

$: \implies \sf{} 22= - x$

$: \implies \underline{\boxed{\sf{} x = - 22}}$

.°. value of x= -22

Now Let's Verify whether value of x is correct or not

$\underline \frak{ \pink{Verification: }}$

$: \implies \sf{}\dfrac{x + 7}{x + 2} = \dfrac{3}{4}$

put value of x in this equation

$: \implies \sf{}\dfrac{ - 22 + 7}{ - 22+ 2} = \dfrac{3}{4}$

$: \implies \sf{}\dfrac{ -15}{ - 20} = \dfrac{3}{4}$

$: \implies \sf{}\dfrac{ \cancel -15}{ \cancel- 20} = \dfrac{3}{4}$

$: \implies \sf{}\dfrac{15}{ 20} = \dfrac{3}{4}$

Divide numerator and denominator by 5

$: \implies \sf{} \cancel\dfrac{15}{ 20} = \dfrac{3}{4}$

$: \implies \sf{} \dfrac{3}{4} = \dfrac{3}{4}$

$: \implies \sf{} \dfrac{3}{4} \times \dfrac{4}{3} = 1$

$: \implies \sf{} \dfrac{12}{12} = 1$

$: \implies \sf{} \cancel \dfrac{12}{12} = 1$

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

$\large{\rm RHS=LHS}$

Hence verified!