A. Incorrect! You did not use the distributive property. The expression in parentheses was ignored.

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1 Problem Solving Drill 06: Simple Equations Question No. 1 of 10 Question 1. Simplify the algebraic expression: 2x(4x 3) Question #01 (A) 2x (B) 8x 6 (C) 8x 2 6x (D) 8x 2 6 You did not use the distributive property. The expression in parentheses was ignored. You only distributed 2 when you should have distributed 2x. C. Correct! The distributive property was used correctly. The x was not multiplied throughout the expression in parentheses. : 2x(4x 3) 2x(4x) + 2x(-3) * use the distributive property 8x 2 2x

2 Question No. 2 of 10 Question 2. Simplify the algebraic expression: 3(y + 3) 2(x + 5y) Question #02 (A) 2x 7y + 9 (B) -2x 7y + 9 (C) 2x 7y + 6 (D) -2x + 13y + 9 Take the sign in front of each number when you multiply. B. Correct! The distributive property was correctly applied and you correctly combined the like terms. C. Incorrect! 3 times 3 is 9 not 6. Use your sign rules when multiplying. : 3(y + 3) 2(x + 5y) Step 1: Get rid of grouping symbols using the distributive property 3y + 9 2x 10y Step 2: Collect like terms 9 2x 10y + 3y Step 3: Rewrite in the simplest form 9 2x 7y Or -2x 7y + 9

3 Question No. 3 of 10 Question 3. Find x satisfying the algebraic equation: 17 + x = 15 Question #03 (A) -2 (B) -32 (C) 32 (D) 2 A. Correct! Subtracted 17 from both side of the equation to get x = -2. Perform the opposite operation on both sides of the equation to isolate the variable. C. Incorrect! Perform the opposite operation on both sides of the equation to isolate the variable. Perform the opposite operation on both sides of the equation to isolate the variable. : 17 + x = x 17 = * Isolate the variable by doing the inverse operation on both sides x = -2

4 Question No. 4 of 10 y Question 4. Solve: 9 =- 18 Question #04 (A) 2 (B) -2 (C) -162 (D) 162 Perform the opposite operation on both sides of the equation to isolate the variable. Perform the opposite operation on both sides of the equation to isolate the variable. C. Correct! Multiply by -18 on both side of the equation to get y = Ignored the negative sign : y 9=- 18 y 9 (-18) = - (-18) 18 * Multiply both sides by = y

5 Question No. 5 of 10 Question 5. Solve: 2x + 7 = 21 Question #05 (A) 14 (B) -28 (C) 7 (D) 2 Perform the opposite operations on both sides of the equation to isolate the variable. Perform the opposite operations on both sides of the equation to isolate the variable. C. Correct! Subtract 7 from both sides and divide by 2 to get x = 7. Perform the opposite operations on both sides of the equation to isolate the variable. : 2x + 7 = * add both sides by -7 2x = 14 2x = * divide both sides by 2 x = 7

6 Question No. 6 of 10 Question 6. Solve: x (4x 15) = 45 Question #06 (A) 20 (B) 10 (C) -10 (D) -20 Simplify the left side then perform the opposite operation on both sides of the equation to isolate the variable. Simplify the left side then perform the opposite operation on both sides of the equation to isolate the variable. C. Correct! Simplify the left side then perform the opposite operation on both sides of the equation to find x = -10. Simplify the left side then perform the opposite operation on both sides of the equation to isolate the variable. : x (4x 15) = 45 x 4x + 15 = 45 x 4x = * Get rid of grouping symbols using the distributive property * Isolate the variable by doing the inverse operation on both sides -3x = 30 * Divide both sides by -3 x = -10

7 Question No. 7 of 10 Question 7. Solve: -x + 3 = 10 Question #07 (A) -9 (B) -7 (C) 7 (D) 9 Isolate variable x on the left using inverse operations on both sides. B. Correct! Get x = -7 by using inverse operations on both sides. C. Incorrect! Isolate variable x on the left using inverse operations on both sides. Isolate variable x on the left using inverse operations on both sides. : -x + 3 = 10 -x = 10 3 * Isolate the variable by doing the inverse operation on both sides -x = 7 x = -7 * Multiply both sides by -1, that is, just change sign

8 Question No. 8 of 10 Question 8. Solve: 6z + 1 = -14 Question #08 (A) -2.5 (B) 2.5 (C) -6.5 (D) 6.5 A. Correct! Perform inverse operations on both sides to get z = Perform inverse operations on both sides to isolate the variable. C. Incorrect! Perform inverse operations on both sides to isolate the variable. Perform inverse operations on both sides to isolate the variable. s: 6z + 1 = -14 6z = * Isolate the variable by doing the inverse operation on both sides 6z = -15 z = -2.5 * Divide both sides by 6

9 Question No. 9 of 10 Question 9. Find the equivalent equation to: 2(3x 1) 3(5x 3) = 4 Question #09 (A) -3x 5 = 4 (B) -9x 11 = 4 (C) -9x 4 = 4 (D) -9x + 7 = 4 Use the distributive property and combine like terms to find the equivalent equation. Use the distributive property and combine like terms to find the equivalent equation. C. Incorrect! Use the distributive property and combine like terms to find the equivalent equation. D. Correct! Use the distributive property and combine like terms to find the equivalent equation of -9x + 7 = 4. : 2(3x 1) 3(5x 3) = 4 6x 2 15x + 9 = 4 6x 15x = 4-9x + 7 = 4 *Answer choice D

10 Question No. 10 of 10 Question 10. Two friends are renting an apartment. They pay the landlord the first month s rent. The landlord also requires them to pay an additional one month s rent for a security deposit. The total amount they pay the landlord before moving in is $1720. What is the monthly rent? Question #10 (A) $172 (B) $430 (C) $860 (D) $1720 Use the given information to create and solve an equation for the situation. Use the given information to create and solve an equation for the situation. C. Correct! Divide the monthly rent by 2 to get $860. Use the given information to create and solve an equation for the situation. : Let x= rent per month, then x + x = x = 1720 x = 860 Thus, the monthly rent for this apartment is $860.