Question

name:
1 solve $2x - 7 = 41$.
2 solve $4(-5x + 15) = 40$.
3 solve $\frac{2}{3}x - 8 = 28$.

Explanation:

Problem 1: Solve \( 2x - 7 = 41 \)

Step 1: Add 7 to both sides

To isolate the term with \( x \), we add 7 to both sides of the equation. This gives us \( 2x - 7 + 7 = 41 + 7 \), which simplifies to \( 2x = 48 \).

Step 2: Divide by 2

Now, we divide both sides by 2 to solve for \( x \). So, \( \frac{2x}{2} = \frac{48}{2} \), which simplifies to \( x = 24 \).

Step 1: Divide by 4

First, we divide both sides of the equation by 4 to simplify. This gives \( \frac{4(-5x + 15)}{4} = \frac{40}{4} \), which simplifies to \( -5x + 15 = 10 \).

Step 2: Subtract 15

Next, we subtract 15 from both sides: \( -5x + 15 - 15 = 10 - 15 \), which simplifies to \( -5x = -5 \).

Step 3: Divide by -5

Finally, we divide both sides by -5: \( \frac{-5x}{-5} = \frac{-5}{-5} \), so \( x = 1 \).

Step 1: Add 8 to both sides

To isolate the term with \( x \), we add 8 to both sides: \( \frac{2}{3}x - 8 + 8 = 28 + 8 \), which simplifies to \( \frac{2}{3}x = 36 \).

Step 2: Multiply by \( \frac{3}{2} \)

To solve for \( x \), we multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \). So, \( \frac{3}{2} \times \frac{2}{3}x = 36 \times \frac{3}{2} \). The left side simplifies to \( x \), and the right side simplifies to \( 54 \).

Answer:

\( x = 24 \)

Problem 2: Solve \( 4(-5x + 15) = 40 \)