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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Here are the solutions to the problems. Question 1: Step 1: Distribute the numbers outside the parentheses to the terms inside. 3(2x-5) + 4(x+3) = (3 × 2x) - (3 × 5) + (4 × x) + (4 × 3) = 6x - 15 + 4x + 12 Step 2: Combine like terms (terms with x and constant terms). = (6x + 4x) + (-15 + 12) = 10x - 3 The correct option is A. The simplified expression is A. 10x - 3. Question 2: Step 1: Solve the equation x-4=7 for x. x - 4 = 7 Add 4 to both sides of the equation. x = 7 + 4 x = 11 Step 2: Substitute the value of x into the expression 2x+3. 2x + 3 = 2(11) + 3 = 22 + 3 = 25 The correct option is not listed among A, B, C, D. Let me recheck my calculation. x-4=7 x=11. 2x+3 = 2(11)+3 = 22+3 = 25. The options are A. 13, B. 17, C. 20, D. 27. My calculated answer is 25, which is not among the options. There might be an error in the question's options. However, I must choose from the given options. I will state my calculated answer and note the discrepancy. Given the strict instruction to choose from the options, and my calculation is 25, which is not an option, I cannot provide a correct option. I will state the correct numerical answer. The value of 2x+3 is 25. (Note: This answer is not among the provided options.) Question 3: Step 1: Isolate the term with x by subtracting 5 from both sides of the equation. (x)/(3) + 5 = 9 (x)/(3) = 9 - 5 (x)/(3) = 4 Step 2: Solve for x by multiplying both sides by 3. x = 4 × 3 x = 12 The correct option is C. The value of x is C. 12. Question 4: Step 1: Find the expression for P - Q. P - Q = (2x^2 - 3x + 1) - (x^2 + 4x - 2) Distribute the negative sign to each term in Q. P - Q = 2x^2 - 3x + 1 - x^2 - 4x + 2 Combine like terms. P - Q = (2x^2 - x^2) + (-3x - 4x) + (1 + 2) P - Q = x^2 - 7x + 3 Step 2: Substitute x=2 into the expression for P - Q. P - Q = (2)^2 - 7(2) + 3 P - Q = 4 - 14 + 3 P - Q = -10 + 3 P - Q = -7 The correct option is not listed among A, B, C, D. Let me recheck my calculation. P - Q = (2x^2 - 3x + 1) - (x^2 + 4x - 2) = 2x^2 - 3x + 1 - x^2 - 4x + 2 = x^2 - 7x + 3. Substitute x=2: (2)^2 - 7(2) + 3 = 4 - 14 + 3 = -10 + 3 = -7. The options are A. 2, B. 4, C. 6, D. 8. My calculated answer is -7, which is not among the options. There might be an error in the question's options. I will state the correct numerical answer. The value of P - Q when x=2 is -7. (Note: This answer is not among the provided options.) Question 5: Step 1: Translate the problem into an algebraic equation. "A number n is increased by 15" can be written as n + 15. "the result is then multiplied by 3" means 3(n + 15). "to give 60" means 3(n + 15) = 60. Step 2: Solve the equation for n. 3(n + 15) = 60 Divide both sides by 3. n + 15 = (60)/(3) n + 15 = 20 Subtract 15 from both sides. n = 20 - 15 n = 5 The correct option is B. The value of n is B. 5. That's 2 down. 3 left today — send the next one.