(a) Solve the inequality. $2x - 1 < 7$ and $3x + 24 \ge 12$ $x \ge 2$ $-4 < x \le 4$ no solution $-2 < x \le 2$ $-4 \le x < 4$ Graph the solution on the number line. + 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Clear All Draw: Write the solution in interval notation. (If there is no solution, enter \"DNE\").
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Step 1: Solve the first inequality: 2x - 1 < 7 2x < 8 x < 4 Show more…
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a) Show that the inequality 6x / (x + 3) ≤ 4 is equivalent to the inequality 2(x - 6) / (x + 3) ≤ 0. b) Sketch the solution on a number line. c) Write the solution using interval notation. 2. a) Solve the inequality for x. 6x / (x + 3) ≤ 4 6x / (x + 3) - 4 ≤ 0 6x / (x + 3) - 4((x + 3) / (x + 3)) ≤ 0 (6x - 4x - 12) / (x + 3) ≤ 0 (2x - 12) / (x + 3) ≤ 0 2(x - 6) / (x + 3) ≤ 0 c) The solution is (-3, 6].
Madhur L.
2. a) Solve the inequality for x. 6x / (x + 3) <= 4, 6x / (x + 3) - 4 <= 0, 6x / (x + 3) - 4(x + 3) / (x + 3) <= 0, (6x - 4x - 12) / (x + 3) <= 0, (2x - 12) / (x + 3) <= 0, 2(x - 6) / (x + 3) <= 0. b) -4 -3 -2 -1 0 1 2 3 4 5 6. c) The solution is (-3, 6].
Adi S.
Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$ 3 x-2>4 \text { or } 5 x-3 \leq 7 $$
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