Question

directions: show your work neatly and clearly, and circle your answers when possible. solve each equation.

1. -5(4 + x)-3(x - 4)=2(x - 4)
2. $\frac{x - 1}{2}+\frac{x}{5}=10$
3. 0.2x + 0.5(17 - x)=7
4. solve the equation for y: 5x + 7y=35
5. solve the following equation for l: 2l + 2w = p
6. find the simple interest earned if $3,000 were invested at a rate of 6% annually for 2 years.

solve each quadratic equation.

1. $x^{2}-x - 56=0$
2. $6x^{2}-13x + 6=0$
3. $z^{2}-5z - 1=0$
4. use the formula p = 2l + 2w to find the length l of a rectangular lot if the width w is 50 feet and the perimeter p is 250 feet.
5. find the real and imaginary parts of the complex number: -2 - 5$sqrt{5}$
6. combine the following complex numbers: (2 + 3i)+(4 + 3i)

Explanation:

Step1: Expand the equation

\[

$$\begin{align*} -5(4 + x)-3(x - 4)&=2(x - 4)\\ -20-5x-3x + 12&=2x-8 \end{align*}$$

\]

Step2: Combine like - terms

\[

$$\begin{align*} -20 + 12-5x-3x&=2x-8\\ -8-8x&=2x-8 \end{align*}$$

\]

Step3: Move variables to one side

Add \(8x\) to both sides: \(-8=2x + 8x-8\), which simplifies to \(-8 = 10x-8\).
Then add 8 to both sides: \(0 = 10x\).

Step4: Solve for \(x\)

Divide both sides by 10, we get \(x = 0\).

Answer:

\(x = 0\)