Question

here is an equation that is true for all values of x:5(x+2)=5x+10. Elena saw this equation and says she can tell 20(x+2)=4(5x+10)+31 is also true for any value of x. How can she tell? Explain your reasoning.

Answer 1

Elena is wrong, because the two sides of equation are not equal for all values of x

Step-by-step explanation:

An equation of x is true for all values of x when the left hand side

is equal to the right hand side

To prove that an equation is true for all values of x do that

• Simplify the left hand side and the right hand side
• Solve the equation to find x, you will find the x in the left hand side is equal to x in the right hand side, so they canceled each other, and the numerical terms in the two sides equal each other, that means the equation is true for any values of x

Lets check that with given equation 5(x + 2) = 5x + 10

∵ 5(x + 2) = 5x + 10

- Simplify the left hand side

∵ 5(x) + 5(2) = 5x + 10

∴ 5x + 10 = 5x + 10

- Subtract 5x from both sides

∴ 10 = 10

∵ L.H.S = R.H.S

∴ The equation is true for all values of x

Lets do that with Elena's equation

∵ 20(x + 2) = 4(5x + 10) + 31

- Simplify the two sides of the equation

∵ 20(x) + 20(2) = 4(5x) + 4(10) + 31

∴ 20x + 40 = 20x + 40 + 31

- Add like terms in the right hand side

∴ 20x + 40 = 20x + 71

- Subtract 20x from both sides

∴ 40 = 71 ⇒ and that not true

∵ L.H.S ≠ R.H.S

∴ The equation is not true for all values of x

Elena is wrong, because the two sides of equation are not equal for all values of x

Learn more:

You can learn more about the equations in brainly.com/question/11306893

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