Question

solve each of the following equations show your work if every number works, write all real numbers if the equation has no solution, write no solution.6-5h=3h + 14-2x - 5 = -13-7 = 1 + n/3-2 (4x-5) + 6 = -(8x+16) 7n - (5+5n) = 15

Answer 1

In order to determine which equations have solution you proceed as follow:

6 - 5h = 3h + 14 subtract 3h and subtract 6 both sides

-5h-3h = 14-6 simplify

-8h = 8 divide by -8 both sides

-8h/(-8) = 8/(-8)

h = -1

Hence, the previous equation has solution

2x - 5 = -13 sum 5 both sides

2x - 5 + 5 = -13 + 5 simplify

2x = -8 divide by 2 both sides

2x/2 = -8/2

x = -4

Hence, the repcious equation has solution

-7 = 1 + n/3 multiply both sides by 3 (to eliminate denominator 3)

-21 = 3 + n sum 3 both sides

-18 = n

the previous one has solution

-2 (4x-5) + 6 = -(8x+16) use distribution property and eliminate parenthesis

(-2)(4x) + (-2)(-5) + 6 = -8x - 16 simplify

-8x + 10 + 6 = -8x - 16 simplify

-8x + 16 = -8x - 16 sum 8x both sides

16 = -16

The previous result is an inconsistency, hence, the previous equation does not have solution.

7n - (5+5n) = 15 eliminate parenthesis

7n - 5 - 5n = 15 simplify and sum 5 both sides

2n = 20 divede by 2 both sides

n =10

The previous equation has solution