Question

geometry concepts
solving equations part 3
solve each equation.

1. 10 + 6x = 4x - 4
2. 14 - 3a = 3a + 2 - 4a
3. -2n + 7n = 8 + 2n + 5n
4. -8x + 2 = 6 - 1 - 7x - 6
5. 22 - 3x = -2 - 2(4x + 8)
6. 17 + 5k = -6(-k - 2)
7. 3n + 3 = 3(n + 1)
8. -3x - 13 = -(-2 - 2x)
9. -3(6x - 6) - 8x = 4(-2 - 8x) - 4
10. 4(4 + n) = 2(n - 1)

Explanation:

Problem 1: \( 10 + 6x = 4x - 4 \)

Step 1: Restar \( 4x \) de ambos lados

\( 10 + 6x - 4x = 4x - 4 - 4x \)
\( 10 + 2x = -4 \)

Step 2: Restar 10 de ambos lados

\( 10 + 2x - 10 = -4 - 10 \)
\( 2x = -14 \)

Step 3: Dividir por 2

\( \frac{2x}{2} = \frac{-14}{2} \)
\( x = -7 \)

Step 1: Simplificar el lado derecho

\( 14 - 3a = -a + 2 \)

Step 2: Sumar \( 3a \) a ambos lados

\( 14 - 3a + 3a = -a + 2 + 3a \)
\( 14 = 2a + 2 \)

Step 3: Restar 2 de ambos lados

\( 14 - 2 = 2a + 2 - 2 \)
\( 12 = 2a \)

Step 4: Dividir por 2

\( \frac{12}{2} = \frac{2a}{2} \)
\( a = 6 \)

Step 1: Simplificar ambos lados

\( 5n = 8 + 7n \)

Step 2: Restar \( 7n \) de ambos lados

\( 5n - 7n = 8 + 7n - 7n \)
\( -2n = 8 \)

Step 3: Dividir por -2

\( \frac{-2n}{-2} = \frac{8}{-2} \)
\( n = -4 \)

Answer:

\( x = -7 \)

Problem 2: \( 14 - 3a = 3a + 2 - 4a \)