Question

ving multistep equations with variables on one side
3 + 5x
(8x - 8) + 3
+ 6 - 5x
4
27 = 1 - 5x + 6
5
-2 = x - 4 + 6
6
2 - 4(1 - 3x) = 82
7
6(x + 6) = 24
8
100 = -5(8x + 4)
9
-152 = -8x - 7(8 - 8x)

Explanation:

Let's solve each equation one by one:

Equation 4: \( 27 = 1 - 5x + 6 \)

Step 1: Combine like terms on the right side

\( 27 = (1 + 6) - 5x \)
\( 27 = 7 - 5x \)

Step 2: Subtract 7 from both sides

\( 27 - 7 = -5x \)
\( 20 = -5x \)

Step 3: Divide both sides by -5

\( x = \frac{20}{-5} \)
\( x = -4 \) (matches the given answer)

Equation 5: \( -2 = x - 4 + 6 \)

Step 1: Combine like terms on the right side

\( -2 = x + ( - 4 + 6) \)
\( -2 = x + 2 \)

Step 2: Subtract 2 from both sides

\( -2 - 2 = x \)
\( x = -4 \)

Equation 6: \( 2 - 4(1 - 3x) = 82 \)

Step 1: Distribute -4 on the left side

\( 2 - 4\times1 + 4\times3x = 82 \)
\( 2 - 4 + 12x = 82 \)

Step 2: Combine like terms on the left side

\( (2 - 4) + 12x = 82 \)
\( -2 + 12x = 82 \)

Step 3: Add 2 to both sides

\( 12x = 82 + 2 \)
\( 12x = 84 \)

Step 4: Divide both sides by 12

\( x = \frac{84}{12} \)
\( x = 7 \)

Equation 7: \( 6(x + 6) = 24 \)

Answer:

s for each equation:

1. \( x = -4 \)
2. \( x = -4 \)
3. \( x = 7 \)
4. \( x = -2 \)
5. \( x = -3 \)
6. \( x = -2 \)