Question

Given that 2x+7=27 and 3x+1=28, does 2x+7=3x+1? Explain.

Answer 1

$\large\sf\underline{Given\::}$

Equation 1 :-

• 2x + 7 = 27

Equation 2 :-

• 3x + 1 = 28

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$\large\sf\underline{To\::}$

• Verify if the given two equations are equal.

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$\large\sf\underline{Concept\::}$

Here we are given two linear equation we need to verify if they are equal. We can do so by solving the given two equation separately. We will first solve them one by one and determine the value of x . After doing so if we get the same value for the variable x , we can say that they are equal. Let's begin !

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$\large\sf\underline{Solution\::}$

Let's calculate the value of x for equation 1 :

$\sf\:2x+7=27$

• Transposing +7 to RHS it becomes -7

$\sf\implies\:2x=27-7$

$\sf\implies\:2x=20$

• Transposing 2 to RHS it goes to the denominator

$\sf\implies\:x=\frac{20}{2}$

• Reducing the fraction to the lower terms

$\sf\implies\:x=\cancel{\frac{20}{2}}$

$\small{\underline{\boxed{\mathrm\red{\implies\:x\:=\:10}}}}$ ★

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Let's calculate the value of x for equation 2 :

$\sf\:3x+1=28$

• Transposing +1 to RHS it becomes -1

$\sf\implies\:3x=28-1$

$\sf\implies\:3x=27$

• Transposing 3 to RHS it goes to the denominator

$\sf\implies\:x=\frac{27}{3}$

• Reducing the fraction to the lower terms

$\sf\implies\:x=\cancel{\frac{27}{3}}$

$\small{\underline{\boxed{\mathrm\red{\implies\:x\:=\:9}}}}$ ★

So cleary for equation 1 we got x as 10 and for equation 2 we got x as 9 .

We do know that :

• 10 ≠ 9

Henceforth we may conclude that :

$\maltese$ $\large{\mathfrak{Equation\:1\:≠\:Equation\:2}}$

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!! Hope it helps !!‎