Question

Why is x = 4 a solution to the proportion 14/x = 56/16

Answer 1

$\large\text{Hey there!}$

$\large\text{Step 1: You have to \underline{\bf{CROSS MULTIPLY}}}$

$\mathsf{\dfrac{14}{x}=\dfrac{56}{16}}\\\\\mathsf{14\times16=56\times x}\\\\\mathsf{14(16)= \ \bf{\underline{224}}}\\\\\mathsf{56(x)=\underline{\bf{56x}}}$

$\huge\text{We get: \bf{\underline{224 = 56x}}}$

$\large\text{Step 2: }\large\text{\bf{\underline{FLIP}}}\large\text{ the new equation around}$

$\huge\text{\bf{\underline{56x = 224}}}$

$\large\text{Step 3: \bf{\underline{DIVIDE}}}\large\text{ both of your sides by 56}$

$\mathsf{\dfrac{56x}{56}=\dfrac{224}{56}}\\\\\mathsf{Cancel\ out: \dfrac{56x}{56}\ because\ that\ gives\ us\ 1}\\\\\mathsf{Keep: \dfrac{224}{56}\ because\ it\ gives you\ the\ value\ of\ x }\\\\\mathsf{\dfrac{224}{56}=4}\\\\\mathsf{x=4}$

$\boxed{\large\text{So, the reason why x = 4 for this equation is because } \mathsf{\dfrac{14}{4}}\ \& \ \dfrac{56}{16}\ \large\text{ are equal to each}}\\\boxed{\large\text{other. }}$

$\mathsf{\dfrac{14}{4} = 3.5}$

$\mathsf{\dfrac{56}{16} = 3.5}$

$\huge\text{\bf{3.5 = 3.5}} \ \checkmark$

$\large\text{Good luck on your assignment and enjoy your day!}$

~$\dag\dfrac{\frak{LoveYourselfFirst}}{:)}$

Answer 2

Answer:

because if you substitute 4 into the equation for x and cross multiply, you get 224 = 224

Step-by-step explanation:

Hope this helps

Have a nice day