Question

solve for the variable.
1 x + 6 = 14
2 y - 9 = 3
3 4a = 20
4 b ÷ 5 = 6
5 m + 11 = 25

Explanation:

Problem 1: \( x + 6 = 14 \)

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 \( a - c = b - c \).
\( x + 6 - 6 = 14 - 6 \)

Step 2: Simplify both sides

Simplifying the left side, \( x + 6 - 6 \) becomes \( x \). Simplifying the right side, \( 14 - 6 = 8 \).
So, \( x = 8 \)

Problem 2: \( y - 9 = 3 \)

Step 1: Add 9 to both sides

To isolate \( y \), we add 9 to both sides of the equation. This is based on the addition property of equality, which states that if \( a = b \), then \( a + c = b + c \).
\( y - 9 + 9 = 3 + 9 \)

Step 2: Simplify both sides

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

Problem 3: \( 4a = 20 \)

Step 1: Divide both sides by 4

To isolate \( a \), we divide both sides of the equation by 4. This is based on the division property of equality, which states that if \( a = b \) and \( c
eq 0 \), then \( \frac{a}{c} = \frac{b}{c} \).
\( \frac{4a}{4} = \frac{20}{4} \)

Step 2: Simplify both sides

Simplifying the left side, \( \frac{4a}{4} \) becomes \( a \). Simplifying the right side, \( \frac{20}{4} = 5 \).
So, \( a = 5 \)

Problem 4: \( b \div 5 = 6 \)

Answer:

s:

1. \( x = 8 \)
2. \( y = 12 \)
3. \( a = 5 \)
4. \( b = 30 \)
5. \( m = 14 \)