Math Peoples. Help me please :)

<ol>
<li>If x-1 is a multiple of 3, which of the following must ne the next greater multiple of 3?
a. x
b. x+2
c. x+3
d. 3x
e. 3x-3</li>
</ol>

<p>The book said it's B. But I say it's c. Because well let's substitute. Lets say x is 4. The next multiple of 3 is 6. So x would equal 7. So the difference of x and the next greater multiple x is 3 (7-4=3). So why isn't it c??</p>

<ol>
<li>For this question, I just want to know if there is a simpler way to solve it:</li>
</ol>

<p>If 3x+y=14, and x and y are positive integers, a;; of the following could be the valur of x=y EXCEPT
a. 4
b. 6
c. 8
d. 10
e. 12</p>

<p>Answer is A</p>

<p>First: Okay, let’s follow your reasoning.</p>

<p>Let’s say x = 4. x-1 is a multiple of 3. Then the next one is 6. 6 = 4+2 = x+2, which is the correct answer. I get the feeling you’re mixing up what x is- x has the same value throughout this question. You want the next multiple in terms of x.</p>

<p>Another way you could do it is not substitute at all: the next multiple of 3 has to be three more, so (x-1)+3 = x+2.</p>

<p>Second: I’m assuming you mean ‘value of x+y’. Well, 3x+y = 2x + (x+y) = 14, so (x+y) = 14 - 2x. So now we’ve got it in terms of x. What can x be? x is a positive integer, so it’s at least 1, and it’s at most 4, because if it were any bigger y would be negative. So 14 - 2x could be 12, 10, 8, or 6 (for x = 1, 2, 3, or 4). 4 is impossible.</p>

<p>Thank you ^^</p>