Show each step of your work and fully simplify each expression.
Turn in your answers in class on a physical piece of paper.
Staple multiple sheets together.
Feel free to use Desmos for graphing.
Answer the following:
Isolate the given variable in the following equations:
$4x + 2 = 6x - w, \ $ for $x$
$\dfrac{x + 1}{x - 3} = 1, \ $ for $x$
$4xy - w(2xz - 3yz) + 3 = -4x - y, \ $ for $x$
$\dfrac{1}{x} - \dfrac{2x}{x^2} - 2 = 4$
Find all real-valued solutions (meaning your solutions must be in $\mathbb{R}$) for the following equations.
$3x + 4 = 7$
$2x + 3 = 7 - 3x$
$x^2 + x - 12 =0$
$2x^2 = 8$
$4x^2 - x = 0$
$x^2 = 3(x-1)$
$\dfrac{1}{x} = \dfrac{4}{3x} + 1$
$\dfrac{1}{x-1} + \dfrac{1}{x+2} = \dfrac{5}{4}$
Isolate $x$ in the equation $a(b + cx) + d = e$. Remember to simplify compound fractions when you see them.
A student tries to isolate $x$ in the equation $(a + b)x = c + d$ by dividing by $a + b$, resulting in \[x = \dfrac{c}{a + b} + d\] What mistake did the student make?
Solve the following equations. Remember to check your work if necessary!
$\dfrac{1}{x-1} - \dfrac{2}{x^2} = 0$
$\sqrt{8x - 1} = 3$
$\sqrt{2x + 1} + 1 = x$
Add, subtract, divide or multiply. Make sure your answer is in the form $a + bi$.
$(3 + 2i) + 5i$
$(-12 + 8i) - (7 + 4i)$
$(5 - 3i)(1 + i)$
$(3 - 7i)^2$
(skip) $\dfrac{1}{i}$
(skip) $\dfrac{2 - 3i}{1 - 2i}$
(skip) $i^{10}$
(skip) Solve $3x^2 + 1 = 0$. Make sure your solution is a complex number.