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Rational Inequalities

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Wize High School Grade 12 Pre-Calculus Textbook > Inequalities

Solving Rational Inequalities (Number Line & Graphs)

5 Activities

Wize High School Algebra II Textbook (Common Core) > Rational Functions

Solving Rational Inequalities (Number Line & Graphs)

5 Activities

Determine an expression for a polynomial, f(x),f(x), that has the following properties:
  • f(x)≤0f(x)\leq{}0 when x≤4x\leq{}4
  • f(x)≥0f(x)\geq{}0 when x≥4x\geq{}4
  • There is an x-intercept at x=−43x=-\dfrac{4}{3} with multiplicity of 5.
  • f(0)=7f(0)=7
Express f(x) f(x)~ in factored form a(x−x1)(x−x2)...(x−xn)a(x-x_1)(x-x_2)...(x-x_n)

More Solving Rational Inequalities (Number Line & Graphs) Questions:
Solving Rational Inequalities
Practice: Solving Rational Inequalities
Solve for x.
∣3x∣>x\Bigg|\dfrac{3}{x}\Bigg|>x
Solving Rational Inequalities
Practice: Solving Rational Inequalities
Solve for x.
∣1x−3∣≥1\Bigg|\dfrac{1}{x-3}\Bigg|\geq{}1
Solving Rational Inequalities
Practice: Solving Rational Inequalities
Find the values of x that make x−2x+4−1<1x\dfrac{x-2}{x+4}-1<\dfrac{1}{x} true.
Solving Rational Inequalities
Practice: Solving Rational Inequalities
Find the values of x that make 5x+9x−1+3>−3x\dfrac{5x+9}{x-1}+3>-\dfrac{3}{x} true.
Solving Rational Inequalities
Practice: Solving Rational Inequalities
The following is a graph of f(x)f(x).
Solve for the following polynomial inequalities. Express the solution in interval notation.
Solving Rational Inequalities
Practice: Solving Rational Inequalities
The following is a graph of f(x)f(x).
Solve for the following polynomial inequalities. Express the solution in interval notation.
Solving Polynomial Inequalities
Solve for bb.
5b+67=b+3b+1\dfrac{5b+6}{7}=\dfrac{b+3}{b+1}
Solving Rational Inequalities
Determine x:x: 3xx2+5x+6<2x+1\dfrac{3x}{x^2+5x+6}<\dfrac{2}{x+1}
Solving Rational Inequalities (Number Line & Graphs)
Solve for a:a:
a−3a2+2a+1≥5a+1\dfrac{a-3}{a^2+2a+1}\geq\dfrac{5}{a+1}
Inequalities
Solve 3x+5≥x2+13x+5\geq{}x^2+1.
More Solving Rational Inequalities (Number Line & Graphs) Questions:
Solving Rational Inequalities
Practice: Solving Rational Inequalities
Solve for x.
∣3x∣>x\Bigg|\dfrac{3}{x}\Bigg|>x
Solving Rational Inequalities
Practice: Solving Rational Inequalities
Solve for x.
∣1x−3∣≥1\Bigg|\dfrac{1}{x-3}\Bigg|\geq{}1
Solving Rational Inequalities
Practice: Solving Rational Inequalities
Find the values of x that make x−2x+4−1<1x\dfrac{x-2}{x+4}-1<\dfrac{1}{x} true.
Solving Rational Inequalities
Practice: Solving Rational Inequalities
Find the values of x that make 5x+9x−1+3>−3x\dfrac{5x+9}{x-1}+3>-\dfrac{3}{x} true.
Solving Rational Inequalities
Practice: Solving Rational Inequalities
The following is a graph of f(x)f(x).
Solve for the following polynomial inequalities. Express the solution in interval notation.
Solving Rational Inequalities
Practice: Solving Rational Inequalities
The following is a graph of f(x)f(x).
Solve for the following polynomial inequalities. Express the solution in interval notation.
Solving Polynomial Inequalities
Solve for bb.
5b+67=b+3b+1\dfrac{5b+6}{7}=\dfrac{b+3}{b+1}
Solving Rational Inequalities
Determine x:x: 3xx2+5x+6<2x+1\dfrac{3x}{x^2+5x+6}<\dfrac{2}{x+1}
Solving Rational Inequalities (Number Line & Graphs)
Solve for a:a:
a−3a2+2a+1≥5a+1\dfrac{a-3}{a^2+2a+1}\geq\dfrac{5}{a+1}
Inequalities
Solve 3x+5≥x2+13x+5\geq{}x^2+1.