We are asked to solve various problems related to real numbers, scientific notation, solving equations, and linear equations. From the section "Solve Equations", two questions from 1-4 should be solved. Let's solve problems 1 and 2. Problem 1: $\frac{1}{3}(x+20) = -9$ Problem 2: $4 - 20x - 5 = -x - 19$

1. Problem Description

We are asked to solve various problems related to real numbers, scientific notation, solving equations, and linear equations. From the section "Solve Equations", two questions from 1-4 should be solved. Let's solve problems 1 and

2.

Problem 1: $\frac{1}{3}(x+20) = -9$

Problem 2: $4 - 20x - 5 = -x - 19$

2. Solution Steps

Problem 1: $\frac{1}{3}(x+20) = -9$

Step 1: Multiply both sides of the equation by 3 to eliminate the fraction.

$3 * \frac{1}{3}(x+20) = 3*(-9)$

$x + 20 = -27$

Step 2: Subtract 20 from both sides of the equation to isolate $x$.

$x + 20 - 20 = -27 - 20$

$x = -47$

Problem 2: $4 - 20x - 5 = -x - 19$

Step 1: Combine like terms on the left side of the equation.

$-20x - 1 = -x - 19$

Step 2: Add $20x$ to both sides of the equation.

$-20x - 1 + 20x = -x - 19 + 20x$

$-1 = 19x - 19$

Step 3: Add 19 to both sides of the equation.

$-1 + 19 = 19x - 19 + 19$

$18 = 19x$

Step 4: Divide both sides of the equation by 19 to isolate $x$.

$\frac{18}{19} = \frac{19x}{19}$

$x = \frac{18}{19}$

3. Final Answer

Solution to Problem 1: $x = -47$

Solution to Problem 2: $x = \frac{18}{19}$