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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