We are just starting this section, and I'm confused...Please help me understand how to solve this inequality:
(one fifth r is less than two)
1/5r < 2
Also, simplify: (the #s are exponents)
z3 . z3
x12/x3
By 1/5r you mean r/5 or 1/(5r)?
z^3 . z^3 = z^6
x^12/x^3 = x^9
If you mean r/5<2, multiply each side by 5, leaving you with r<10. If you mean 1/(5r)<2, multiply each side by 5r, leaving you with 1<10r. Then divide each side by 10 and r>1/10.
To solve the inequality (1/5r < 2), we need to isolate the variable "r" on one side of the inequality symbol.
If by 1/5r you mean r/5, then the inequality can be rewritten as:
r/5 < 2
To solve for "r", we can multiply both sides of the inequality by 5, which gives us:
5 * (r/5) < 2 * 5
This simplifies to:
r < 10
So, if 1/5r means r/5, the solution is r < 10.
On the other hand, if by 1/5r you mean 1/(5r), then the inequality becomes:
1/(5r) < 2
To eliminate the fraction, we can multiply both sides by 5r:
5r*(1/(5r)) < 2*(5r)
This simplifies to:
1 < 10r
To isolate "r", we can divide both sides of the inequality by 10, giving us:
1/10 < r
So, if 1/5r means 1/(5r), the solution is 1/10 < r.
For the simplification questions:
z^3 . z^3 can be simplified by adding the exponents since we are multiplying the same base:
z^(3+3) = z^6
Thus, z^3 . z^3 simplifies to z^6.
For x^12/x^3, we can simplify by subtracting the exponents since we are dividing the same base:
x^(12-3) = x^9
Thus, x^12/x^3 simplifies to x^9.