Answer: x = -1/4
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Step-by-step explanation:
You have the right idea to multiply everything by 10 to clear out the fractions.
You did the (1/10x)*10 part correctly. That evaluates to 1x or simply x.
However, the part with (1/5)10 is not correct. The result for this piece isn't 50. Instead, it should be 2. You can think of it as 10/5 = 2.
Also, the (1/2x)10 should evaluate to 5x. You can think of it like 10x/2 = 5x.
Lastly, the (3/10)10 part should result in 3. The 10s cancel leaving just the 3.
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This is what your steps could look like.
(1/10x + 1/5 = 1/2x + 3/10)*10
(1/10x)*10 + (1/5)*10 = (1/2x)*10 + (3/10)*10
x + 2 = 5x + 3
2-3 = 5x-x
-1 = 4x
4x = -1
x = -1/4