Solve each equation.

Understand the Problem

The document contains a series of multi-step algebraic equations that need to be solved. Each equation represents a mathematical problem that requires finding the value of one or more variables.

Answer

1. $ x = 2 $ 2. $ n = 0 $ 3. $ x = -7 $ 4. $ a = 0 $ 5. $ m = 4 $ 6. $ p = 1 $

Steps to Solve

Equation (1): Solve for x in $-20 = -4x - 6x$

Combine the like terms on the right side: $$ -20 = (-4x - 6x) = -10x $$

Now, divide both sides by -10 to isolate $x$: $$ x = \frac{-20}{-10} = 2 $$

Equation (2): Solve for y in $6 = 1 - 2n + 5$

First, simplify the right side: $$ 6 = 6 - 2n $$

Subtract 6 from both sides: $$ 0 = -2n $$

Now, divide by -2: $$ n = 0 $$

Equation (3): Solve for x in $8x - 2 = -9 + 7x$

Add 9 to both sides: $$ 8x - 2 + 9 = 7x $$

This simplifies to: $$ 8x + 7 = 7x $$

Subtract $7x$ from both sides: $$ 8x - 7x = -7 $$

This simplifies to: $$ x = -7 $$

Equation (4): Solve for a in $a + 5 = -5a + 5$

Add $5a$ to both sides: $$ a + 5 + 5a = 5 $$

Combine like terms: $$ 6a + 5 = 5 $$

Now, subtract 5 from both sides: $$ 6a = 0 $$

Finally, divide by 6: $$ a = 0 $$

Equation (5): Solve for m in $5m - 4 = 4m$

Add $4$ to both sides: $$ 5m = 4 + 4m $$

Now subtract $4m$: $$ 5m - 4m = 4 $$

This simplifies to: $$ m = 4 $$

Equation (6): Solve for p in $p - 1 = 5p + 3p - 8$

Combine the terms on the right side: $$ p - 1 = 8p - 8 $$

Add 1 to both sides: $$ p = 8p - 7 $$

Now subtract $8p$: $$ -7p = -7 $$

Divide by -7: $$ p = 1 $$

( x = 2 )
( n = 0 )
( x = -7 )
( a = 0 )
( m = 4 )
( p = 1 )

More Information

These equations are examples of solving for variables in multi-step algebraic equations. Each equation requires isolating the variable through arithmetic operations. The process demonstrates fundamental principles of algebra, emphasizing the importance of balancing equations while manipulating them to find solutions.

Tips

Forgetting to combine like terms correctly.
Neglecting to change the sign when moving terms from one side of the equation to the other.
Misapplying the distributive property when expanding expressions.

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