directions: solve each compound or double - inequality and then match the problem up with the graph of its…
directions: solve each compound or double - inequality and then match the problem up with the graph of its solution.\n1. solve: (x + 2>4) and (x - 1<4)\n2. solve: (0leq x + 3leq5)\n3. solve: (2 + xleq2) or (2-3xgeq - 4)\n4. solve: (4xleq - 12) and (\frac{x}{2}leq1)\n5. solve: (\frac{x}{2}+3leq1) or (\frac{5x}{4}-1>\frac{3}{2})\n6. solve: (2x - 5<5) or (3x + 1>-2)
Answer
Explanation:
Step1: Solve (x + 2>4)
Subtract 2 from both sides: (x>4 - 2), so (x>2).
Step2: Solve (x - 1<4)
Add 1 to both sides: (x<4 + 1), so (x<5). The solution is (2<x<5), which matches graph d.
Answer: d
Explanation:
Step1: Solve (0\leq x + 3)
Subtract 3 from both sides: (x\geq0 - 3), so (x\geq - 3).
Step2: Solve (x + 3\leq5)
Subtract 3 from both sides: (x\leq5 - 3), so (x\leq2). The solution is (-3\leq x\leq2), which matches graph b.
Answer: b
Explanation:
Step1: Solve (2 + x\leq2)
Subtract 2 from both sides: (x\leq2 - 2), so (x\leq0).
Step2: Solve (2-3x\geq - 4)
Subtract 2 from both sides: (-3x\geq - 4 - 2), so (-3x\geq - 6). Divide both sides by - 3 and reverse the inequality sign: (x\leq2). The solution of the "or" - compound inequality is (x\leq2), which matches graph i.
Answer: i
Explanation:
Step1: Solve (4x\leq - 12)
Divide both sides by 4: (x\leq\frac{-12}{4}), so (x\leq - 3).
Step2: Solve (\frac{x}{2}\leq1)
Multiply both sides by 2: (x\leq2). The solution of the "and" - compound inequality is (x\leq - 3), which matches graph h.
Answer: h
Explanation:
Step1: Solve (\frac{x}{2}+3\leq1)
Subtract 3 from both sides: (\frac{x}{2}\leq1 - 3), so (\frac{x}{2}\leq - 2). Multiply both sides by 2: (x\leq - 4).
Step2: Solve (\frac{5x}{4}-1>\frac{3}{2})
Add 1 to both sides: (\frac{5x}{4}>\frac{3}{2}+1), so (\frac{5x}{4}>\frac{3 + 2}{2}=\frac{5}{2}). Multiply both sides by (\frac{4}{5}): (x>2). The solution of the "or" - compound inequality is (x\leq - 4) or (x>2), which matches graph f.
Answer: f
Explanation:
Step1: Solve (2x-5<5)
Add 5 to both sides: (2x<5 + 5), so (2x<10). Divide both sides by 2: (x<5).
Step2: Solve (3x + 1>-2)
Subtract 1 from both sides: (3x>-2 - 1), so (3x>-3). Divide both sides by 3: (x>-1). The solution of the "or" - compound inequality is all real numbers, which matches graph g.