Compare the process of solving an equation and an inequality. What are the differences and the similarities?

1 answer:

7 0

when you solve an inequality the result is an interval when you solve an equation is a number or set ex x^2=25 x=-+5 the result is finite numbers

when you multimply an equation the sign inverses but when you solve an equation there is nothing to change

similiarities

you can add and subtract numbers from both sides

diving and multypling the equation or inequation by a positive numeber as i said in the beggining by multypling or dividing with a negative number the equation s sign inverses ex >= becomes <=

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You borrow 125,000 for 25 years at an APR of 6.5%. What will be your monthly payment?

Morgarella [4.7K]

$\bf \qquad \qquad \textit{Amortized Loan Value}
\\\\
pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right]
\\\\\\\\
\qquad 
\begin{cases}
P=
\begin{array}{llll}
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\end{array}\to &
\begin{array}{llll}
125000
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8 0

2 years ago

Solve for x: 4 over x plus 4 over quantity x squared minus 9 equals 3 over quantity x minus 3. (2 points) Select one: a. x = -4

Kay [80]

Answer:

Step-by-step explanation:

$\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}$

Domain:

$x\neq0\ \wedge\ x^2-9\neq0\ \wedge\ x-3\neq0\\\\x\neq0\ \wedge\ x\neq\pm3$

solution:

$\dfrac{4}{x}+\dfrac{4}{x^2-3^2}=\dfrac{3}{x-3}$

use (a - b)(a + b) = a² - b²

$\dfrac{4}{x}+\dfrac{4}{(x-3)(x+3)}=\dfrac{3}{x-3}$

multiply both sides by (x - 3) ≠ 0

$\dfrac{4(x-3)}{x}+\dfrac{4(x-3)}{(x-3)(x+3)}=\dfrac{3(x-3)}{x-3}$

cancel (x - 3)

$\dfrac{4(x-3)}{x}+\dfrac{4}{x+3}=3$

subtract $\frac{4(x-3)}{x}$ from both sides

$\dfrac{4}{x+3}=3-\dfrac{4(x-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x}{x}-\dfrac{(4)(x)+(4)(-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-\bigg(4x-12\bigg)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-4x-(-12)}{x}\\\\\dfrac{4}{x+3}=\dfrac{-x+12}{x}$