Question

solving one step equations with addition and subtraction
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solve each equation. show all work.

1. $x + 6 = -10$
2. $10 = v - (-14)$
3. $n + (-6) = 6$
4. $23 = 15 + a$
5. $k - (-6) = 2$
6. $x - (-18) = 1$
7. $13 = x + 2$
8. $-10 + n = -2$
9. $11 + m = 6$
10. $-17 = p - (-1)$
11. $-8 = x - 19$
12. $7 + n = 14$

Explanation:

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

Step 1: Subtract 6 from both sides

To isolate \( x \), we subtract 6 from both sides of the equation. This is based on the subtraction property of equality, which states that if \( a = b \), then \( a - c = b - c \).
\( x + 6 - 6 = -10 - 6 \)

Step 2: Simplify both sides

Simplifying the left side, \( x + 6 - 6 \) becomes \( x \). Simplifying the right side, \( -10 - 6 = -16 \).
\( x = -16 \)

Step 1: Simplify the double negative

Recall that subtracting a negative is the same as adding a positive, so \( v - (-14) = v + 14 \). The equation becomes \( 10 = v + 14 \).

Step 2: Subtract 14 from both sides

Using the subtraction property of equality, subtract 14 from both sides to isolate \( v \).
\( 10 - 14 = v + 14 - 14 \)

Step 3: Simplify both sides

Simplifying the left side, \( 10 - 14 = -4 \). Simplifying the right side, \( v + 14 - 14 = v \).
\( v = -4 \)

Step 1: Simplify the left side

Adding a negative is the same as subtracting, so \( n + (-6) = n - 6 \). The equation becomes \( n - 6 = 6 \).

Step 2: Add 6 to both sides

Using the addition property of equality, add 6 to both sides to isolate \( n \).
\( n - 6 + 6 = 6 + 6 \)

Step 3: Simplify both sides

Simplifying the left side, \( n - 6 + 6 = n \). Simplifying the right side, \( 6 + 6 = 12 \).
\( n = 12 \)

Answer:

\( x = -16 \)

Problem 2: \( 10 = v - (-14) \)