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# Solving Basic Algebra Equations Practice Questions (page 2)

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Updated on Sep 23, 2011

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Numerical expressions in parentheses like this [ ] are operations performed on only part of the original expression. The operations performed within these symbols are intended to show how to evaluate the various terms that make up the entire expression.

Expressions with parentheses that look like this ( ) contain either numerical substitutions or expressions that are part of a numerical expression. Once a single number appears within these parentheses, the parentheses are no longer needed and need not be used the next time the entire expression is written.

When two pair of parentheses appear side by side like this ( )( ), it means that the expressions within are to be multiplied.

Sometimes parentheses appear within other parentheses in numerical or algebraic expressions. Regardless of what symbol is used, ( ), { }, or [ ], perform operations in the innermost parentheses first and work outward.

Underlined equations show the simplified result.

 1. Subtract 21 from both sides of the equation. Associate like terms. a + (21 – 21) = (32 – 21) Perform the numerical operation in the parentheses. a + (0) = (11) Zero is the identity element for addition. a = 11 2. Add 25 to each side of the equation. 25 + x – 25 = 32 + 25 Use the commutative property for addition. x + 25 – 25 = 32 + 25 Associate like terms. x + (25 – 25) = (32 + 2/td> Perform the numerical operation in the parentheses. x + (0) = (57) Zero is the identity element for addition. x = 57 3. Subtract 17 from both sides of the equation. y + 17 – 17 = –12 – 17 Associate like terms. y + (17 – 17) = (–12 – 17) Change subtraction to addition and change the sign of the term that follows. y + (17 + –17) = (–12 + –17) Apply the rules for operating with signed numbers. y + (0) = –29 Zero is the identity element for addition. 3. Change subtraction to addition and change the sign of the term that follows. b + –15 = 71 Add +15 to each side of the equation. b + –15 + +15 = 71 + +15 Associate like terms. b + (–15 + 15) = (71 + 15) Apply the rules for operating with signed numbers. b + (0) = 86 Zero is the identity element for addition. b = 86 4. Change subtraction to addition and change the sign of the term that follows. b + –15 = 71 Add +15 to each side of the equation. b + –15 + +15 = 71 + +15 Associate like terms. b + (–15 + 15) = (71 + 15) Apply the rules for operating with signed numbers. b + (0) = 86 Zero is the identity element for addition. b = 86 5. Change subtraction to addition and change the sign of the term that follows. 12 + –c = –9 Add +c to each side of the equation. 12 + –c + +c = –9 + +c 12 + –c + +c = –9 + +c 12 + (–c + +c) = –9 + +c 12 + (0) = –9 + c 12 = –9 + c Add +9 to each side of the equation. +9 + 12 = +9 + –9 + c Associate like terms./td> (+9 + 12) = (+9 + –9) + c Apply the rules for operating with signed numbers. (21) = (0) + c Zero is the identity element for addition. 21 = c 6. Change subtraction to addition and change the sign of the term that follows. s + +4 = –1 Add –4 to each side of the equation. s + +4 + –4 = –1 + –4 Associate like terms. s + (+4 + –4) = –1 + –4 Apply the rules for operating with signed numbers. s + (0) = (–5) Subtracting zero is the same as adding zero. s = –5 7. Add to each side of the equation. Associate like terms. Apply the rules for operating with signed numbers. Zero is the identity element for addition. 8. Change subtraction to addition and change the sign of the term that follows. Subtract from both sides of the equation. Associate like terms. Change subtraction to addition and change the sign of the term that follows. Apply the rules for operating with signed numbers. Change the improper fraction to a mixed number. 9. Change subtraction to addition and change the sign of the term that follows. Use the distributive property of multiplication. Perform the operation in parentheses. c + (–2 + +20) = 20 Apply the rules for operating with signed numbers. c + (–2 + +20) = 20 Subtract 18 from both sides of the equation. c + (18) = 20 Associate like terms. c + 18 – 18 = 20 – 18 Perform the operation in parentheses. c + (18 – 18) = 20 – 18 Zero is the identity element for addition. c = 2 10. Use the distributive property of multiplication. m + (2 · 5 – 2 · 24) = –76 The order of operations is to multiply first. m + (10 – 48) = –76 Add +38 to each side of the equation. m + –38 + +38 = –76 + +38 Associate like terms. m + (–38 + +38) = –76 + +38 Apply the rules for operating with signed numbers. m + (0) = –38 11. Divide both sides of the equation by 2. 2a ÷ 2 = 24 ÷ 2 a = 24 ÷ 2 Apply the rules for operating with signed numbers. a = 12 Another method is as follows: a = 12 12. Divide both sides of the equation by 4. 4x ÷ 4 = –20 ÷ 4 x = –20 ÷ 4 Apply the rules for operating with signed numbers. Another look for this solution method is as follows: 13. Divide both sides of the equation by –3. Apply the rules for operating with signed numbers. 14. Divide both sides of the equation by 27. Reduce fractions to their simplest form. 15. Divide both sides of the equation by 45. Reduce fractions to their simplest form (common factor of 15). 16. Divide both sides of the equation by 0.2. Divide. c = 29 17. Multiply both sides of the equation by 7. x = 7(16) Multiply. x = 112 18. Multiply both sides of the equation by –4. y = –4 · –12 Signs the same? Multiply and give the result a positive sign. y = +48 = 48 19. Divide both sides of the equation by Dividing by a fraction is the same as multiplying by its reciprocal. a = 81 20. Divide both sides of the equation by Dividing by a fraction is the same as multiplying by its reciprocal. There are several ways to multiply fractions and whole numbers. Here's one. 21. Let x = the suggested selling price of the car. The first and second sentences tell you that of the suggested price = \$21,000. So your equation is: Divide both sides of the equation by Dividing by a fraction is the same as multiplying by its reciprocal. x = \$24,000 22. Let b = the number of bears in each packing crate. The first sentence tells you that the number of packing crates times the number of bears in each is equal to the total number of bears. Your equation is: 54b = 324 Divide both sides of the equation by 54. 54b ÷ 54 = 324 ÷ 54 b = 324 ÷ 54 Divide. b = 6 23. Let t = the number of turtle hatchlings born. The first sentence tells you that only 3% survive to adulthood. Three percent of the turtles born is 1,200. Your equation will be: (3%)t = 1,200 The numerical equivalent of 3% is 0.03, so the equation becomes 0.03t = 1,200. Divide both sides of the equation by 0.03. 0.03t ÷ 0.03 = 1,200 ÷ 0.03 t = 1,200 ÷ 0.03 Divide. t = 40,000 24. Let c = the number of acres he planted last year. 1.5 times c is 300. 1.5c = 300 Divide both sides of the equation by 1.5. 1.5c ÷ 1.5 = 300 ÷ 1.5 c = 300 ÷ 1.5 Divide. c = 200 25.Let d = her annual salary. Five percent of her salary equals her yearly bonus. Your equation will be: (5%)d = \$6,000 The numerical equivalent of 5% is 0.05, so the equation becomes 0.05d = 6,000. Divide both sides of the equation by 0.05. 0.05d ÷ 0.05 = 6,000 ÷ 0.05 d = 6,000 ÷ 0.05 Divide. d = \$120,000
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