Question

lesson 1 assignment

1. $4x = 20x - 24$ \\(\quad\\) $x = \underline{\quad\quad}$
2. $-2x - 1.4 = 6 + 3x$ \\(\quad\\) $x = \underline{\quad\quad}$

Explanation:

Problem 7: \( 4x = 20x - 24 \)

Step 1: Subtract \( 20x \) from both sides

To isolate the variable terms, we subtract \( 20x \) from both sides of the equation. This gives us:
\( 4x - 20x = 20x - 20x - 24 \)
Simplifying the left side and the right side, we get:
\( -16x = -24 \)

Step 2: Divide both sides by -16

To solve for \( x \), we divide both sides of the equation by \( -16 \):
\( x = \frac{-24}{-16} \)
Simplifying the fraction, we find that \( \frac{-24}{-16} = \frac{3}{2} = 1.5 \)

Step 1: Add \( 2x \) to both sides

To get all the variable terms on one side, we add \( 2x \) to both sides of the equation:
\( -2x + 2x - 1.4 = 6 + 3x + 2x \)
Simplifying the left side and the right side, we have:
\( -1.4 = 6 + 5x \)

Step 2: Subtract 6 from both sides

Next, we subtract 6 from both sides to isolate the term with \( x \):
\( -1.4 - 6 = 6 - 6 + 5x \)
Simplifying the left side and the right side, we get:
\( -7.4 = 5x \)

Step 3: Divide both sides by 5

To solve for \( x \), we divide both sides of the equation by 5:
\( x = \frac{-7.4}{5} \)
Calculating the division, we find that \( \frac{-7.4}{5} = -1.48 \)

Answer:

\( x = 1.5 \) (or \( x = \frac{3}{2} \))

Problem 8: \( -2x - 1.4 = 6 + 3x \)