Basic Algebra Equations Quiz

Solving: x + 7 = 12 Subtract 7 from both sides: x + 7 − 7 = 12 − 7 Simplify: x = 5 Answer: x = 5 Core concept: isolate x by undoing addition.

Solving: 3y = 21 Divide both sides by 3: 3y ÷ 3 = 21 ÷ 3 Simplify: y = 7 Answer: y = 7 Core concept: Isolate y by undoing multiplication with division.

Solving: 2z - 5 = 11 Add 5 to both sides: 2z = 16 Divide by 2: z = 8 Answer: z = 8 Core Concept : Reverse the order of operations.

Solving: 4a = a + 15 Subtract 'a' from both sides: 4a - a = 15 3a = 15 Divide by 3: a = 5 Answer: a = 5 Multiple Choice Options (Common Mistakes): ✅ 5 (Correct answer) ❌ 3 (Divided 15 by 4 instead of 3 after subtraction) ❌ 15 (Ignored the variable term 'a' on the right side, solving 4a=15) ❌ 4 (Subtracted 15-4a instead of collecting like terms) Core Concept: Move all variable terms to one side first, then solve like a two-step equation.

Solving: 3(b + 2) = 18 Distribute the 3: 3b + 6 = 18 Subtract 6 from both sides: 3b = 12 Divide by 3: b = 4 Answer: b = 4 Multiple Choice Options (Common Mistakes): ✅ 4 (Correct answer) ❌ 6 (Forgot to distribute, solved b + 2 = 18/3) ❌ 2 (Distributed incorrectly as 3b + 2 = 18) ❌ 5 (Divided 18 by 3 first, then subtracted 2) Core Concept: Always distribute before isolating the variable!

Solving: 2c + 5 + c = 20 Combine like terms: 3c + 5 = 20 Subtract 5 from both sides: 3c = 15 Divide by 3: c = 5 Answer: c = 5 Multiple Choice Options (Common Mistakes): ✅ 5 (Correct answer) ❌ 7.5 (Added all terms: 2c + c + 5 = 3c + 5 = 20 → 3c = 20 - 5 = 15 → c = 5, but mistakenly divided 15 by 2) ❌ 15 (Ignored the variable terms, solved 5 = 20 - c → c = 15) ❌ 10 (Forgot to combine terms, solved 2c = 20 - 5 → c = 7.5, then added c = 7.5 + 2.5) Core Concept: Always combine like terms before isolating the variable!

Solving: 2(d + 3) = d + 10 Distribute the 2: 2d + 6 = d + 10 Subtract d from both sides: d + 6 = 10 Subtract 6 from both sides: d = 4 Answer: d = 4 Multiple Choice Options (Common Mistakes): ✅ 4 (Correct answer) ❌ 7 (Distributed incorrectly as 2d + 3 = d + 10) ❌ 2.5 (Subtracted 6 from 10 first, then divided by 2) ❌ 16 (Multiplied all terms by 2: 4d + 6 = 2d + 20 → d = 16) Core Concept : Distribute first, then get all variable terms to one side!

Solving: ½x - 4 = 8 Add 4 to both sides: ½x = 12 Multiply both sides by 2: x = 24 Answer: x = 24 Multiple Choice Options (Common Mistakes): ✅ 24 (Correct answer) ❌ 6 (Multiplied ½x × 4 instead of adding 4) ❌ 16 (Solved ½x = 8 - 4 but forgot to multiply by 2) ❌ 4 (Divided all terms by ½: x - 8 = 16 → x = 24, but misapplied steps) Core Concept : Eliminate fractions last - first isolate the fractional term!

Solving: 0.3y + 2 = 3.2 Subtract 2 from both sides: 0.3y = 1.2 Divide both sides by 0.3: y = 4 Answer: y = 4 Multiple Choice Options (Common Mistakes): ✅ 4 (Correct answer) ❌ 1.5 (Multiplied 0.3 × 3.2 instead of subtracting 2 first) ❌ 0.36 (Multiplied 0.3 × 1.2 instead of dividing) ❌ 40 (Multiplied by 10 to eliminate decimal but forgot to adjust other terms) Core Concept: Treat decimal coefficients like whole numbers - just watch your decimal placement!

Solving: 2(3f - 1) + 4 = 16 Distribute the 2: 6f - 2 + 4 = 16 Combine like terms: 6f + 2 = 16 Subtract 2 from both sides: 6f = 14 Divide by 6: f = 14⁄6 = 7⁄3 Answer: f = 7⁄3 or 21⁄3 Multiple Choice Options (Common Mistakes): ✅ 7⁄3 (Correct answer) ❌ 3 (Forgot to distribute, solved 3f - 1 + 4 = 16) ❌ 2 (Distributed incorrectly as 6f - 1 + 4 = 16) ❌ 14⁄3 (Forgot to combine -2 + 4 before solving) Core Concept: Distribute completely before combining terms!

Solving: ⅔g = g - 5 Subtract ⅔g from both sides: 0 = ⅓g - 5 Add 5 to both sides: 5 = ⅓g Multiply both sides by 3: g = 15 Answer: g = 15 Multiple Choice Options (Common Mistakes): ✅ 15 (Correct answer) ❌ 3 (Solved ⅔g = g - 5 as 5 = ⅓g but then divided 5 by ⅓ incorrectly) ❌ 10 (Multiplied all terms by 3 first but made an error: 2g = 3g - 5 → g = 5) ❌ 7.5 (Treated equation as ⅔g = 5 → g = 7.5) Core Concept: Eliminate fractions by multiplying ALL terms by the denominator when needed!"

Solving: 3(h + 2) = 2(h - 1) Distribute both sides: 3h + 6 = 2h - 2 Subtract 2h from both sides: h + 6 = -2 Subtract 6 from both sides: h = -8 Answer: h = -8 Multiple Choice Options (Common Mistakes): ✅ -8 (Correct answer) ❌ 4 (Distributed incorrectly: 3h + 2 = 2h - 1 → h = -3) ❌ -4 (Forgot to distribute right side: 3h + 6 = h - 1 → h = -3.5) ❌ 8 (Sign error: solved as 3h + 6 = 2h + 2 → h = -4) Core Concept: Distribute carefully to ALL terms inside parentheses before solving!

Solving: (2k/3) + ½ = 5 Subtract ½ from both sides: 2k/3 = 4½ Convert to improper fraction: 2k/3 = 9/2 Cross-multiply: 4k = 27 Divide by 4: k = 27/4 or 6¾ Answer: k = 27⁄4 (or 6.75) Multiple Choice Options (Common Mistakes): ✅ 27⁄4 (Correct answer) ❌ 13⁄2 (Forgot to convert 4½ to 9/2, solved 2k/3 = 4.5 → k = 6.75) ❌ 9⁄4 (Multiplied all terms by 3 first but forgot to multiply the 5) ❌ 15⁄2 (Multiplied all terms by 6 but made arithmetic errors) Core Concept: Clear fractions early by multiplying by the LCD, or work carefully with equivalent fractions!

Solving: 4(m + 1) - 2 = 3m + m + 6 Distribute the 4: 4m + 4 - 2 = 3m + m + 6 Combine like terms on both sides: 4m + 2 = 4m + 6 Subtract 4m from both sides: 2 = 6 Identify the contradiction: No solution (∅) Answer: No solution (∅) Multiple Choice Options (Common Mistakes): ✅ No solution (Correct answer) ❌ 0 (Miscalculated: 4m + 2 = 4m + 6 → 0 = 4) ❌ 4 (Added terms incorrectly: 4m + 2 = 7m + 6 → m = -4/3) ❌ All real numbers (Misinterpreted 2 = 6 as always true) Core Concept: When variables cancel out, the resulting statement determines if there's no solution or infinite solutions!

Solving: 0.25(3n + 8) = ½n - 1 Convert all terms to fractions: ¼(3n + 8) = ½n - 1 Distribute ¼: ¾n + 2 = ½n - 1 Multiply all terms by 4 (LCD): 3n + 8 = 2n - 4 Subtract 2n from both sides: n + 8 = -4 Subtract 8 from both sides: n = -12 Answer: n = -12 Multiple Choice Options (Common Mistakes): ✅ -12 (Correct answer) ❌ -4 (Multiplied only some terms by 4: ¾n + 8 = ½n - 4 → n = -12) ❌ 4 (Sign error: solved as 3n + 8 = -2n - 4 → n = -2.4) ❌ -6 (Decimal error: treated 0.25 as ¼ but ½n as 0.5n → arithmetic mistakes) Core Concept: Convert all terms to the same form (fractions or decimals) before solving, and consistently apply operations to ALL terms!