Question

4 - 20 + 6n = - 8+3n
6 $\frac{x + 3}{4}=x$

Explanation:

1. Solve the equation \(-20 + 6n=-8 + 3n\):

• Step 1: Move the terms with \(n\) to one - side
• Subtract \(3n\) from both sides of the equation.

\(-20 + 6n-3n=-8 + 3n-3n\)
\(-20 + 3n=-8\)

• Step 2: Move the constant terms to the other side
• Add \(20\) to both sides of the equation.

\(-20+20 + 3n=-8 + 20\)
\(3n = 12\)

• Step 3: Solve for \(n\)
• Divide both sides of the equation by \(3\).

\(\frac{3n}{3}=\frac{12}{3}\)
\(n = 4\)

1. Solve the equation \(\frac{x + 3}{4}=x\):

• Step 1: Multiply both sides by \(4\) to get rid of the fraction
• \(4\times\frac{x + 3}{4}=4x\)

\(x + 3=4x\)

• Step 2: Move the terms with \(x\) to one - side
• Subtract \(x\) from both sides.

\(x - x+3=4x - x\)
\(3 = 3x\)

• Step 3: Solve for \(x\)
• Divide both sides by \(3\).

\(\frac{3}{3}=\frac{3x}{3}\)
\(x = 1\)

Answer:

For \(-20 + 6n=-8 + 3n\), \(n = 4\); for \(\frac{x + 3}{4}=x\), \(x = 1\)