Question

X/3+x/2=1 3-x/5=x/6 x/2-6=x/6

Answer 1

X/3+x/2=1

3-x/5=x/6

x/2-6=x/6

x1=6/5

x2=18/11

x3=18

Answer 2

Let's solve each of these equations step by step:

1. $\frac{X}{3} + \frac{X}{2} = 1$

To solve this equation, first, we need to find a common denominator for the fractions. The common denominator is 6. So, we can rewrite the equation as:

$\frac{2X}{6} + \frac{3X}{6} = 1$

Now, add the fractions together:

$\frac{5X}{6} = 1$

To isolate X, multiply both sides by the reciprocal of $\frac{5}{6}$ (which is $\frac{6}{5}$):

$X = \frac{6}{5}$

2. $3 - \frac{X}{5} = \frac{X}{6}$

Let's get rid of the fractions by multiplying both sides by the least common multiple (LCM) of 5 and 6, which is 30:

$30 \cdot 3 - 30 \cdot \frac{X}{5} = 30 \cdot \frac{X}{6}$

$90 - 6X = 5X$

Now, move the terms with X to one side:

$5X + 6X = 90$

$11X = 90$

Finally, divide both sides by 11 to find the value of X:

$X = \frac{90}{11}$

3. $\frac{X}{2} - 6 = \frac{X}{6}$

First, let's make the denominators the same. The common denominator is 6:

$\frac{3X}{6} - \frac{36}{6} = \frac{X}{6}$

Now, combine the terms with X on one side:

$3X - 36 = X$

Subtract X from both sides:

$3X - X = 36$

$2X = 36$

Divide by 2 to find X:

$X = \frac{36}{2}$

$X = 18$

So, the solutions to the given equations are:

1. $X = \frac{6}{5}$
2. $X = \frac{90}{11}$
3. $X = 18$