Question

circle the equations for which 6 is a solution of the equation.
$4x=2$
$y - 2 = 4$
$6z = 36$
$12\div w = 6$
$x + 2 = 6$
$56 = 5y$
$8 + z = 14$
$2 = \frac{w}{12}$

Explanation:

To determine for which equations 6 is a solution, we substitute \( x = 6 \) (or the relevant variable) into each equation and check if it holds true. Let's analyze each equation:

1. \( y - 2 = 4 \)

Substitute \( y = 6 \):
\( 6 - 2 = 4 \)
\( 4 = 4 \) (True).

2. \( 12 \div w = 6 \)

Substitute \( w = 6 \):
\( 12 \div 6 = 6 \)
\( 2 = 6 \) (False).

3. \( 6z = 36 \)

Substitute \( z = 6 \):
\( 6 \times 6 = 36 \)
\( 36 = 36 \) (True).

4. \( z = \frac{w}{12} \) (Unclear variable, but if we assume \( z = 6 \)):

\( 6 = \frac{w}{12} \implies w = 72 \). Not relevant to \( w = 6 \), but if \( w = 6 \):
\( z = \frac{6}{12} = 0.5
eq 6 \) (False).

5. \( 56 = 5y \)

Substitute \( y = 6 \):
\( 56 = 5 \times 6 \implies 56 = 30 \) (False).

6. \( 8 + z = 14 \)

Substitute \( z = 6 \):
\( 8 + 6 = 14 \implies 14 = 14 \) (True).

Final Answer:

The equations where 6 is a solution are:
\( \boldsymbol{y - 2 = 4} \), \( \boldsymbol{6z = 36} \), and \( \boldsymbol{8 + z = 14} \).

Answer:

To determine for which equations 6 is a solution, we substitute \( x = 6 \) (or the relevant variable) into each equation and check if it holds true. Let's analyze each equation:

1. \( y - 2 = 4 \)

Substitute \( y = 6 \):
\( 6 - 2 = 4 \)
\( 4 = 4 \) (True).

2. \( 12 \div w = 6 \)

Substitute \( w = 6 \):
\( 12 \div 6 = 6 \)
\( 2 = 6 \) (False).

3. \( 6z = 36 \)

Substitute \( z = 6 \):
\( 6 \times 6 = 36 \)
\( 36 = 36 \) (True).

4. \( z = \frac{w}{12} \) (Unclear variable, but if we assume \( z = 6 \)):

\( 6 = \frac{w}{12} \implies w = 72 \). Not relevant to \( w = 6 \), but if \( w = 6 \):
\( z = \frac{6}{12} = 0.5
eq 6 \) (False).

5. \( 56 = 5y \)

Substitute \( y = 6 \):
\( 56 = 5 \times 6 \implies 56 = 30 \) (False).

6. \( 8 + z = 14 \)

Substitute \( z = 6 \):
\( 8 + 6 = 14 \implies 14 = 14 \) (True).

Final Answer:

The equations where 6 is a solution are:
\( \boldsymbol{y - 2 = 4} \), \( \boldsymbol{6z = 36} \), and \( \boldsymbol{8 + z = 14} \).