Question

Solving Inequalities graphically: Use a graphing device to solve the inequality x^{4}+x^{3}\leq5x^{2}+4x-5

Decimals
ANSWERED
asked 2021-08-10
Solving Inequalities Graphically: Use a graphing device to solve the inequality. Express your answer using interval notation, with the endpoints of the interval rounded to two decimals.
\(\displaystyle{x}^{{{4}}}+{x}^{{{3}}}\leq{5}{x}^{{{2}}}+{4}{x}-{5}\)

Expert Answers (1)

2021-08-11
Step 1
Consider the following inequality,
\(\displaystyle{x}^{{{4}}}+{x}^{{{3}}}\leq{5}{x}^{{{2}}}+{4}{x}-{5}\)
Subtract both sides of the equation \(\displaystyle{5}{x}^{{{2}}}+{4}{x}-{5}\) to get the following,
\(\displaystyle{x}^{{{4}}}+{x}^{{{3}}}-{5}{x}^{{{2}}}-{4}{x}+{5}\leq{0}\)
By using software to get the value of \(\displaystyle{x}\approx{0.74},\ {x}\approx{1.95}\)
Use graphing device to get the following,
image
From the above graph \(\displaystyle{x}\in{\left[{0.74},\ {1.95}\right]}\)
So, the solution is \(\displaystyle{x}\in{\left[{0.74},\ {1.95}\right]}\)
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