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3 years ago

14+y = 3y+2, Find y with a step-by-step explanation.

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

6 0

Answer:

y= 6

Step-by-step explanation:

1. Rearrange the terms before the equal sign: 14+y=3y+2-> y+14=3y+2

2. Subtract 14 from both sides: y+14=3y+2-> y=3y-12

-14 -14

3. Subtract 3y from both sides: y=3y-12-> y-3y= -12

-3y -3y

4. Combine like terms: y-3y= -12-> -2y= -12

1-3 keep the y

5. Divide both sides by -2: -2y= -12-> y= 6

/2 /2

6. So, you're left with y= 6

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Find x?<br> In 3x - In(x - 4) = ln(2x - 1) +ln3

earnstyle [38]

Answer:

$x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Step-by-step explanation:

Because $3\, x$ is found in the input to a logarithm function in the original equation, it must be true that $3\, x > 0$ . Therefore, $x > 0$ .

Similarly, because $(x - 4)$ and $(2\, x - 1)$ are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, $x > 4$ .

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Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

$\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}$

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