6. Solve the following inequalities algebraically. Represent your solution on a number line.\ a) $2(x-2)>6$\ b) $3x \ge 5x-8$\ c) $-1 \le -x+9 \le 11$\ 7. Solve the following inequalities using a number line strategy or a factor table strategy. Express\ your answers using set notation.\ a) $(x+4)(x+2)(x-3) \le 0$\ b) $(x+3)^2(x+1)(x-1)>0$\ c) $(x+1)(x+3) \ge 0$\ d) $(x+5)^2(x+2) < 0$
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Step 1: Solve the inequality 2(x-2) > 6 2(x-2) > 6 2x - 4 > 6 2x > 10 x > 5 Show more…
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(a) Use a graph /as in Example 7 (a) 1 to determine which of the following general forms describes the solution set of the given inequality: $$\left[\begin{array}{ll}a, b\end{array}\right] \quad(-\infty, a) \cup(b, \infty) \quad[a, \infty) \quad(a, \infty)$$ (b) Use a graphing utility [as in Example 7(b)] to estimate to the nearest hundredth the value of a, and where appropriate, b. (c) Solve the inequality algebraically and write the solution set using interval notation. Check that your answers are consistent with the graphical results in parts (a) and (b). $$6-13 x<0$$
Equations and Inequalities
Inequalities
Solve the given inequalities. Write the solution set in three ways: a) Graphed on a number line b) Using interval notation c) Using inequality notation $$ x^{2}+7 x+10>0 $$
Quadratic Functions
Solving Equations by Factoring
(a) Use a graph /as in Example 7 (a) 1 to determine which of the following general forms describes the solution set of the given inequality: $$\left[\begin{array}{ll}a, b\end{array}\right] \quad(-\infty, a) \cup(b, \infty) \quad[a, \infty) \quad(a, \infty)$$ (b) Use a graphing utility [as in Example 7(b)] to estimate to the nearest hundredth the value of a, and where appropriate, b. (c) Solve the inequality algebraically and write the solution set using interval notation. Check that your answers are consistent with the graphical results in parts (a) and (b). $$7 x-2 \geq 0$$
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