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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
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 \(3 + 4x < x + 24\)?