Section 2.1 : Solutions and Solution Sets
For each of the following determine if the given number is a solution to the given equation or inequality.
- Is \(u = - 1\) a solution to \(4{u^2} - 40 = 10\left( {2u - 1} \right) - 6\)?
- Is \(t = 7\) a solution to \(7\left( {t + 2} \right) = 5\left( {t + 4} \right) + 2\)?
- Is \(\displaystyle z = - \frac{1}{3}\) a solution to \(6\left( {z - 1} \right) + 5 = 9z\)?
- Is \(x = - 6\) a solution to \({x^2} = - 10x - 24\)?
- Is \(\displaystyle t = \frac{1}{4}\) a solution to \(3{t^2} + 8t = 3\left( {1 - t} \right)\)?
- Is \(w = - 3\) a solution to \(2{w^2} - 10 = {w^2} - 7w + 8\)?
- Is \(\displaystyle x = \frac{1}{2}\) a solution to \(\displaystyle \frac{3}{x} - \frac{1}{{{x^2}}} = 2\)?
- Is \(v = - 2\) a solution to \(\displaystyle \frac{{{v^2} + v - 2}}{{v - 1}} = 0\)?
- Is \(v = 1\) a solution to \(\displaystyle \frac{{{v^2} + v - 2}}{{v - 1}} = 0\)?
- Is \(x = - 1\) a solution to \(\displaystyle \frac{{3x + 1}}{{{x^2}}} - \frac{6}{{x + 2}} = \frac{{x - 7}}{{3x + 4}}\)?
- Is \(y = 4\) a solution to \(4{y^2} - {y^3} \le 5y + 2\)?
- Is \(w = 0\) a solution to \(3\left( {w - 7} \right) + 2\left( {w + 1} \right) > 10w\)?
- Is \(x = 7\) a solution to \(3 + 4x < x + 24\)?