A. Incorrect! Perform inverse operations to find the solution. B. Correct! Add 1 to both sides of the equation then divide by 2 to get x = 5.
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1 Test-Prep Math - Problem Drill 07: The Multi-Step Equations Question No. 1 of Solve: 2x 1 = 9 Question #01 (A) 4 (B) 5 (C) 1/5 (D) -5 (E) 0 B. Correct! Add 1 to both sides of the equation then divide by 2 to get x = 5. x=0 can t be right since it will make the equation into -1=9. s: 2x 1 = 9 2x = To isolate variable, add one on both side of the equation. 2x = 10 To get variable x by itself, divide by 2 on both side of the equation. x = 5 The correct answer is (B).
2 Question No. 2 of Solve: 3x + 1 = -2x 19 Question #02 (A) 4 (B) -20 (C) -18 (D) -4 (E) None of the above D. Correct! Subtract 1 from both sides, add 2x, then divide by 5 to get x = -4. There is indeed a correct answer above. : 3x + 1 = -2x 19 Step 1: Subtract 1 from both sides of the equation. 3x + 1 1= -2x 19 1 Step 2: Simplify the equation. Then add 2x on both sides of the equation. 3x = -2x 20 3x + 2x = -2x + 2x -20 Step 3: Rewrite in the simplest form 5x = -20 x = -4 Divided by 5 to get x by itself. The correct answer is (D).
3 Question No. 3 of Rewrite 75% as a ratio. (A) 1 4 Question #03 (B) (C) 3 4 (D) (E) 1 Review how to write percents as a ratio. Review how to write percents as a ratio. C. Correct! 75% equals ¾. Review how to write percents as a ratio. That would be 100%. : % = = Rewrite 75% into ratio using the definition of percent. Then divide 25 on the numerator and denominator to get the simplified form. The correct answer is (C).
4 Question No. 4 of Solve: 2y = 3y 20 Question #04 (A) -20 (B) -4 (C) 4 (D) 20 (E) 1 D. Correct! Combine the y-terms and divide by -1 to get y = 20. Plug y=1, the equation will become 2=-17, which is incorrect. : 2y = 3y 20 2y 3y = 3y 3y 20 * Subtract 3y from both sides of equation. -y = -20 * Combine the like term -1-1 y = 20 * Divide both sides of the equation by -1 The correct answer is (D).
5 Question No. 5 of 10 Instruction: (1) Read the problem and answer choices carefully (2) Work the problems on paper as 5. Solve: x 6 = 8 16 Question #05 (A) 3 (B) 48 (C) -3 (D) 2 (E) 6 A. Correct! The ratio 6 16 simplifies to 3. 8 Set the product of the extremes equal to the product of the means, then solve. Set the product of the extremes equal to the product of the means, then solve. Set the product of the extremes equal to the product of the means, then solve. Check the ratio. Simplify the ratio on the right and the answer should be apparent. : x 6 = x = 48 * Take cross product. x = 3 * Divide both sides by 16. The correct answer is (A).
6 Question No. 6 of Which equation does NOT have -2 as a solution? Question #06 (A) 2x + 5 = 5x + 11 (B) 3x + 6 4x = x + 10 (C) 7y + 9 = 3 9y (D) 4 + 3y = 7y + 12 (E) 2y = -4 This equation has a solution of -2. This equation has a solution of -2. C. Correct! This equation does not have a solution of -2. This equation has a solution of -2. This simple one-step equation has a solution of -2. Find the answer by using the backward mapping. You substitute -2 for all the variables and find an answer that does not satisfy since the question is asking that the two sides of equation are not balanced. The correct answer is (C).
7 Question No. 7 of Find the constant of variation: y = -7x Question #07 (A) -7x (B) -7 (C) 7 (D) 9 (E) -1 This is not a constant of variation since it includes a variable. B. Correct! By definition, -7 is the constant of variation. The sign is wrong. This is not the constant of variation. This is not the constant of variation since the 7 is in front of the variable x. : By definition, the number in front of the variable x is the constant of variation. Therefore -7 is the correct answer. The correct answer is (B).
8 Question No. 8 of Lauren needs to solve the equation 5 x -3 =2. What should she do first? 3 Question #08 (A) Multiply each side of the equation by 2. (B) Multiply each side of the equation by 3. (C) Subtract 2 from each side of the equation. (D) Cancel the 3 in the numerator and the 3 in the denominator. (E) Nothing. Multiplying 2 on each side of the equation does not simplify the equation. B. Correct! By multiplying 3, you can eliminate the fraction. Subtracting 2 does not make this equation any simpler. You cannot cancel numerator and denominator when there is + or sign. No work no credit. It takes effort to solve problems. Follow what you have learned and step through it. : 5x - 3 =2 3 5x - 3 (3) = 2(3) 3 the fraction. 5x 3 = 6 5x = * Multiply 3 on both sides of the equation. This will eliminate * Add 3 on both sides of the equation. 5x = 9 * Divide both side of the equation by 5. x = 9/5 The correct answer is (B).
9 Question No. 9 of Find 25% of 200. Question #09 (A) 500 (B) 5000 (C) 50 (D) 800 (E) -50 Review how to find the percents of a number. Review how to find the percents of a number. C. Correct! 25% times 200 is 50. Review how to find the percents of a number. Use the common sense. A fraction of a positive number is still positive. : 25 = x * Set up the problem as proportion = 100x * Take the cross product to eliminate the fractions = 100x 50 = x The correct answer is (C).
10 Question No. 10 of 10 Instruction: (1) Read the problem and answer choices carefully (2) Work the problems on paper as 10. Solve: 20% of what number is 40? Question #10 (A) 20 (B) 16 (C) 160 (D) 200 (E) None of the above Setup a proportion to find the value. Setup a proportion to find the value. Setup a proportion to find the value. D. Correct! 20 % of 200 is 40. There is one correct answer above. Step by step complete solution (the long version). This can be any format, whatever you can type in Word = 100 x * Rewrite the problem as proportion. 20 x = * Take the cross product. 20x = 4000 * Divide both sides of the equation by 20. x = 200 The correct answer is (D).
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