Question

one-step equations: integers add/sub level 1: s1 solve each equation. 1) ( x + 9 = 12 ) insert text here 2) ( s - 1 = 10 ) 3) ( 3 = z - 11 ) 4) ( 5 + y = 7 )

Explanation:

Problem 1: Solve \( x + 9 = 12 \)

Step 1: Subtract 9 from both sides

To isolate \( x \), we subtract 9 from both sides of the equation. This is based on the subtraction property of equality, which states that if \( a = b \), then \( a - c = b - c \).
\( x + 9 - 9 = 12 - 9 \)

Step 2: Simplify both sides

Simplifying the left side, \( x + 9 - 9 \) becomes \( x \). Simplifying the right side, \( 12 - 9 = 3 \).
So, \( x = 3 \)

Step 1: Add 1 to both sides

To isolate \( s \), we add 1 to both sides of the equation. This is based on the addition property of equality, which states that if \( a = b \), then \( a + c = b + c \).
\( s - 1 + 1 = 10 + 1 \)

Step 2: Simplify both sides

Simplifying the left side, \( s - 1 + 1 \) becomes \( s \). Simplifying the right side, \( 10 + 1 = 11 \).
So, \( s = 11 \)

Step 1: Add 11 to both sides

To isolate \( z \), we add 11 to both sides of the equation. This is based on the addition property of equality.
\( 3 + 11 = z - 11 + 11 \)

Step 2: Simplify both sides

Simplifying the left side, \( 3 + 11 = 14 \). Simplifying the right side, \( z - 11 + 11 \) becomes \( z \).
So, \( z = 14 \)

Answer:

\( x = 3 \)

Problem 2: Solve \( s - 1 = 10 \)