Question

question 4 of 6
drag each equation to the correct location on the table.
solve the equations for the given variable. then place the equations in the table under the correct solution.

x = 3	x ≠ 3

\\(\frac{x}{3} = 9\\) \\(-6 + x = -9\\) \\(x - 5 = -2\\) \\(-\frac{3}{5} + x = \frac{12}{5}\\) \\(\frac{x}{4} = \frac{6}{8}\\) \\(-14x = -42\\)

Explanation:

To solve this, we'll solve each equation for \( x \) and then categorize them.

Equation 1: \( \frac{x}{3} = 9 \)

Step 1: Multiply both sides by 3

\( x = 9 \times 3 \)
\( x = 27 \) (so \( x
eq 3 \))

Equation 2: \( -6 + x = -9 \)

Step 1: Add 6 to both sides

\( x = -9 + 6 \)
\( x = -3 \) (so \( x
eq 3 \))

Equation 3: \( x - 5 = -2 \)

Step 1: Add 5 to both sides

\( x = -2 + 5 \)
\( x = 3 \) (so \( x = 3 \))

Equation 4: \( -\frac{3}{5} + x = \frac{12}{5} \)

Step 1: Add \( \frac{3}{5} \) to both sides

\( x = \frac{12}{5} + \frac{3}{5} \)
\( x = \frac{15}{5} \)
\( x = 3 \) (so \( x = 3 \))

Equation 5: \( \frac{x}{4} = \frac{6}{8} \)

Step 1: Simplify \( \frac{6}{8} = \frac{3}{4} \)

Step 2: Multiply both sides by 4

\( x = \frac{3}{4} \times 4 \)
\( x = 3 \) (so \( x = 3 \))

Equation 6: \( -14x = -42 \)

Step 1: Divide both sides by -14

\( x = \frac{-42}{-14} \)
\( x = 3 \) (so \( x = 3 \))

Now, categorize:

• \( x = 3 \): \( x - 5 = -2 \), \( -\frac{3}{5} + x = \frac{12}{5} \), \( \frac{x}{4} = \frac{6}{8} \), \( -14x = -42 \)
• **\( x

eq 3 \)**: \( \frac{x}{3} = 9 \), \( -6 + x = -9 \)

Final Categorization:

| \( x = 3 \) | \( x
eq 3 \) |

\( x - 5 = -2 \)	\( \frac{x}{3} = 9 \)
\( -\frac{3}{5} + x = \frac{12}{5} \)	\( -6 + x = -9 \)
\( \frac{x}{4} = \frac{6}{8} \)
\( -14x = -42 \)

Answer:

To solve this, we'll solve each equation for \( x \) and then categorize them.

Equation 1: \( \frac{x}{3} = 9 \)

Step 1: Multiply both sides by 3

\( x = 9 \times 3 \)
\( x = 27 \) (so \( x
eq 3 \))

Equation 2: \( -6 + x = -9 \)

Step 1: Add 6 to both sides

\( x = -9 + 6 \)
\( x = -3 \) (so \( x
eq 3 \))

Equation 3: \( x - 5 = -2 \)

Step 1: Add 5 to both sides

\( x = -2 + 5 \)
\( x = 3 \) (so \( x = 3 \))

Equation 4: \( -\frac{3}{5} + x = \frac{12}{5} \)

Step 1: Add \( \frac{3}{5} \) to both sides

\( x = \frac{12}{5} + \frac{3}{5} \)
\( x = \frac{15}{5} \)
\( x = 3 \) (so \( x = 3 \))

Equation 5: \( \frac{x}{4} = \frac{6}{8} \)

Step 1: Simplify \( \frac{6}{8} = \frac{3}{4} \)

Step 2: Multiply both sides by 4

\( x = \frac{3}{4} \times 4 \)
\( x = 3 \) (so \( x = 3 \))

Equation 6: \( -14x = -42 \)

Step 1: Divide both sides by -14

\( x = \frac{-42}{-14} \)
\( x = 3 \) (so \( x = 3 \))

Now, categorize:

• \( x = 3 \): \( x - 5 = -2 \), \( -\frac{3}{5} + x = \frac{12}{5} \), \( \frac{x}{4} = \frac{6}{8} \), \( -14x = -42 \)
• **\( x

eq 3 \)**: \( \frac{x}{3} = 9 \), \( -6 + x = -9 \)

Final Categorization:

| \( x = 3 \) | \( x
eq 3 \) |

\( x - 5 = -2 \)	\( \frac{x}{3} = 9 \)
\( -\frac{3}{5} + x = \frac{12}{5} \)	\( -6 + x = -9 \)
\( \frac{x}{4} = \frac{6}{8} \)
\( -14x = -42 \)