Question #2b76d

2 Answers
Feb 14, 2017

In this case, the set of like terms are #3/5x# and #7/8x#. To combine them, let's subtract #3/5x# from both sides. On the left side, the positive and negative #3/5x# cancel each other out or become equal to #0#.
#3/5x -(3/5x + 33 = 7/8x)- 3/5x#

So this is how our solution looks like.
#33 = 7/8x - 3/5x#

Let's focus on those two fractions. We'll be subtracting dissimilar fractions. First, we find the LCD (Least Common Denominator) of #8# and #5#, which is #40#.
#7/8x - 3/5x = -/40#

Next, we divide #40# by #8# and #5#. Then, the quotient of #40# and #8# is #5# and will be multiplied to #7#. The quotient of #40# and #5# is #8# and will be multiplied by #3#. The solution looks like this:
#7/8x - 3/5x = (35-24)/40#

Subtract 35 and 24 to get the following:
#33 = 11/40x#

Now let's isolate the variable #x#. We could apply cross-multiplication by multiplying #33# by #40#, #11# by #1# (which is underneath #33# this whole time). Solution becomes like this:
#33/1 = 11/40x# ==> #1320 = 11x#

DIvide both sides by #11# to get #x = 120#.
#1320/11 = 11/11x# ==> #120 = x#

Feb 14, 2017

# x = 120#

Explanation:

#3/"5" .x + 33 = 7/"8".x#

Now, subtracting #3/"5".x # from the both sides

#cancel(3/"5".x) + 33 -cancel( 3/"5".x) = 7/"8".x - 3/"5".x#

#33 = x. (7/"8" - 3/"5")#

#33 = x. ("7(5) - 3(8)"/"40")#

#33 = x. ("35 - 24"/"40")#

#33 = x. 11/"40"#

Multiplying the both sides by 40
#33 × 40 = x. 11/cancel("40" )× cancel(40)#

#33 × 40 = x. 11#

Now, dividing the both sides by 11

#cancel"(33)"^3 × 40/cancel"(11)" = x. cancel"(11)"/cancel"(11)"#

#3 × 40 = x#

#120 = x#