12 1/10
A quick way to get this one is to recognize that .1 is a decimal in the tenth place. Because of this, we know to put it over 10. Because 1/10 cannot be simplified, it is in simplest form. Now, simply return the whole number to the fraction.
Let <em>q</em> be the number of quarts of pure antifreeze that needs to be added to get the desired solution.
8 quarts of 40% solution contains 0.40 × 8 = 3.2 quarts of antifreeze.
The new solution would have a total volume of 8 + <em>q</em> quarts, and it would contain a total amount of 3.2 + <em>q</em> quarts of antifreeze. You want to end up with a concentration of 60% antifreeze, which means
(3.2 + <em>q</em>) / (8 + <em>q</em>) = 0.60
Solve for <em>q</em> :
3.2 + <em>q</em> = 0.60 (8 + <em>q</em>)
3.2 + <em>q</em> = 4.8 + 0.6<em>q</em>
0.4<em>q</em> = 1.6
<em>q</em> = 4
The mathematical expression for x is is fewer than 9 is x< 9
Answer: x = 0
Step-by-step explanation:
1 - 3x = 3x + 1
then add 3x on both sides
1 = 6x + 1
then subtract 1 on both sides
0 = 6x
then divide by 6 on both sides
0 = x
so x = 0
