Are the equations sometimes, always, or never true?

1 answer:

4 0

15 + 2x - 4 = 9x + 11 - 7x
2x + 11 = 2x + 11
always true

2x + 3(4x - 1) = 2(5x + 3) + 4x
2x + 12x - 3 = 10x + 6 + 4x
14x - 3 = 14x + 6
never true

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What is the value of x?

WINSTONCH [101]

Answer:

$\large\boxed{x=8\sqrt2}$

Step-by-step explanation:

$\bold{METHOD\ 1}\\\\\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\ leg=8,\ leg=8,\ hypotenuse=x.\\\text{Substitute:}\\\\x^2=8^2+8^2\\\\x^2=2(8^2)\to x=\sqrt{2(8^2)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x=\sqrt2\cdot\sqrt{8^2}\qquad\text{use}\ \sqrt{a^2}=a\\\\x=8\sqrt2$