This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — Here are some inequality problems in a multiple-choice format, similar to what you might see in an exam. I'll solve each one step-by-step. --- Question 1: Solve the inequality for x: 3x - 8 < 10 A) x < 2 B) x > 2 C) x < 6 D) x > 6 Step 1: Add 8 to both sides of the inequality to isolate the term with x. 3x - 8 + 8 < 10 + 8 3x < 18 Step 2: Divide both sides by 3. Since 3 is a positive number, the inequality sign remains the same. (3x)/(3) < (18)/(3) x < 6 The correct option is C) x < 6. --- Question 2: Solve the inequality for y: -2y + 5 15 A) y -5 B) y -5 C) y 10 D) y 10 Step 1: Subtract 5 from both sides of the inequality. -2y + 5 - 5 15 - 5 -2y 10 Step 2: Divide both sides by -2. Since -2 is a negative number, you must reverse the direction of the inequality sign. (-2y)/(-2) (10)/(-2) y -5 The correct option is B) y -5. --- Question 3: Solve the inequality for z: 5z - 4 2z + 11 A) z 5 B) z 5 C) z (7)/(3) D) z (7)/(3) Step 1: Subtract 2z from both sides to gather the z terms on one side. 5z - 4 - 2z 2z + 11 - 2z 3z - 4 11 Step 2: Add 4 to both sides to isolate the term with z. 3z - 4 + 4 11 + 4 3z 15 Step 3: Divide both sides by 3. Since 3 is a positive number, the inequality sign remains the same. (3z)/(3) (15)/(3) z 5 The correct option is A) z 5. --- Hope these examples help you practice! What's next?