Solving Linear Equations

Solve for the variable.  $\frac{n}{5}\ =\ -2$  

• Add five to both sides.  n = 3

• Subtract five from both sides.  n = -7

• Multiply both sides by five.  n = -10

• Divide both sides by five.  n = -2/5

Solve for the variable. 3n + 11 = -16

• Add 11, then divide by 3; answer is n = -5/3

• Subtract 11, then subtract 3; answer is n = -30

• Subtract 11, then divide by 3; answer is n = 9

• Subtract 11, then divide by 3; answer is n = -9

Solve for the variable. 6 = 1 - n

• Subtract 1; answer is n = 5.

• Subtract 1, divide by -1; answer is n = -5

• Add 1; answer is n = 7.

Which math steps would NOT solve this equation?
 $\frac{3}{2}\left(x\ -\ 2\right)\ -\ 5\ =\ 19$  

• Add 5, Multiply by 2/3, add 2.

• Distribute the 3/2, add 8, divide by 3/2.

• Multiply by 2, add 14, divide by 3.

• Add 5, Add 3/2, Add 2.

Solve the equation for the variable.
 $\frac{3}{2}\left(n\ -\ 2\right)\ -\ 5\ =\ 19$  

• n = 15

• n = 16

• n = 17

• n = 18

Solve the equation for the variable.
 $6\ =\ \frac{1}{5}n\ +\ \frac{7}{5}n\ -\ 4$  

• Multiply by 5, add 4, divide by 8; n = 5/4

• Multiply by 5, add 20, divide by 8; n = 50/8 = 25/4 = 6.25

• Combine like terms, add 4, multiply by 5/8; n = 50/8 = 6.25 

• Add 4, combine like terms, multiply by 5/8.  n = 6.25

Solve for the variable.

5(1 + n) = 5n + 5

• Distribute, both sides are the same; no solutions.

• Distribute, 6n = 5n + 5, so n = 5.

• Distribute, 5 + 5n = 5n + 5, identical so infinitely many solutions

Solve for the variable.
 $3\left(n\ +\ 4\right)\ =\ \frac{1}{2}\left(6n\ +\ 4\right)$  

• Distribute, 3n + 4 = 3n + 4 so infinitely many solutions

• Distribute, 3n + 12 = 3n + 2, never true so no solutions.

• Distribute, n + 12 = 3n + 2, 2n = 10 so n = 5

Solve the equation for n.
 $-3n\ +\ 6\ =\ 2n\ -4$  

• n = -2

• n = 2

• n = 0

• n = 2/5

Translate into algebra:

'Four more than a number equals ten.'

• 4n = 10

• n + 4 = 10

• 4 + n = 10