How do you solve #\frac { 5} { 6} h - \frac { 7} { 12} = - \frac { 3} { 4} h - \frac { 13} { 6}#?

2 Answers
Kalyanam S.
Jul 13, 2018

#color(maroon)(h = -1#

Explanation:

#(5/6)h - 7/12 = -(3/4)h -13/6#

#(5/6)h + (3/4)h = 7/12 - 13/6#

#((10 + 9)/cancel12)h = (7-26)/cancel12#

#19h = -19#

#color(maroon)(h = -1#

Jim G.
Jul 13, 2018

#h=-1#

Explanation:

#"multiply through by the lowest common multiple of"#
#"the denominators, that is 4, 6 and 12"#

#"the lowest common multiple is "12#

#cancel(12)^2xx5/cancel(6)^1h-cancel(12)xx7/cancel(12)=-cancel(12)^3xx3/cancel(4)^1h-(cancel(12)^2xx13/cancel(6)^1)#

#10h-7=-9h-26larrcolor(blue)"no fractions"#

#"add "9h" to both sides"#

#19h-7=-26#

#"add 7 to both sides"#

#19h=-26+7=-19#

#"divide both sides by 19"#

#h=(-19)/19=-1#

#color(blue)"As a check"#

Substitute this value into the equation and if both sides are equal then it is the solution.

#"left "=-5/6-7/12=-17/12#

#"right "=3/4-13/6=-17/12#

#h=-1" is the solution"#

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