Question

solving algebraic equations

1. $8x - 2 = -9 + 7x$
2. $-8 = -(x + 4)$
3. $-(7 - 4x) = 9$
4. $x - 1 = 5x + 3x - 8$
5. $2(4x - 3) - 8 = 4 + 2x$
6. $3x - 5 = -6(6 + 5x)$

Explanation:

Problem 26: \( 8x - 2 = -9 + 7x \)

Step 1: Subtract \( 7x \) from both sides

\( 8x - 7x - 2 = -9 + 7x - 7x \)
\( x - 2 = -9 \)

Step 2: Add 2 to both sides

\( x - 2 + 2 = -9 + 2 \)
\( x = -7 \)

Step 1: Distribute the negative sign

\( -8 = -x - 4 \)

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

\( -8 + x = -x + x - 4 \)
\( x - 8 = -4 \)

Step 3: Add 8 to both sides

\( x - 8 + 8 = -4 + 8 \)
\( x = 4 \)

Step 1: Distribute the negative sign

\( -7 + 4x = 9 \)

Step 2: Add 7 to both sides

\( -7 + 7 + 4x = 9 + 7 \)
\( 4x = 16 \)

Step 3: Divide both sides by 4

\( \frac{4x}{4} = \frac{16}{4} \)
\( x = 4 \)

Answer:

\( x = -7 \)

Problem 27: \( -8 = -(x + 4) \)