Question #2b76d

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Question #2b76d

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Answer 1 · 2017-02-14T17:30:40

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

So this is how our solution looks like.
$33 = \frac{7}{8} x - \frac{3}{5} x$ $33 = 7/8x - 3/5x$

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

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

Subtract 35 and 24 to get the following:
$33 = \frac{11}{40} x$ $33 = 11/40x$

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

DIvide both sides by $11$ $11$ to get $x = 120$ $x = 120$ .
$\frac{1320}{11} = \frac{11}{11} x$ $1320/11 = 11/11x$ ==> $120 = x$ $120 = x$

Answer 2 · 2017-02-14T19:13:54

$x = 120$ $x = 120$

Explanation:

$\frac{3}{5} . x + 33 = \frac{7}{8} . x$ $3/"5" .x + 33 = 7/"8".x$

Now, subtracting $\frac{3}{5} . x$ $3/"5".x$ 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

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

$3 × 40 = x$

$120 = x$

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