Algebra · Chapter 2 of 20

Linear equations

43 curated · 193 from open sources

Before you startAI-drafted · not yet reviewed by an editor

To solve a linear equation, isolate the variable $x$ by doing the same operation to both sides. First simplify each side: distribute to remove parentheses and combine like terms. Then move all terms containing $x$ to one side and all constant terms to the other by adding or subtracting. Finally divide by the coefficient of $x$ . For example, if you reach $4 x = 12$ , divide both sides by $4$ to get $x = 3$ . Check your answer by substituting it back into the original equation.

All Easy Medium Deep

Curated

#	Title	Difficulty	Tags
929	Find x from a duplicate ratio condition	Medium	Duplicate ratioProportion
931	Number to add to a ratio	Medium	RatioAdjustment
932	Proving an Algebraic Ratio Identity	Medium	ratioproportion+1
933	Continued Proportion Identity	Medium	continued proportionalgebraic manipulation+1
934	Symmetric Ratio Relation	Medium	ratiosymmetry+1
936	Fractional Sum with Cubes	Medium	ratiosubstitution+1
937	Reciprocal proportionality	Medium	proportionalitysymmetry
938	Equality case of Cauchy–Schwarz	Medium	Cauchy–Schwarzproportionality
939	Cyclic proportionality	Medium	cyclic symmetryratios
941	Eliminate variables from a three‑equation system	Medium	determinantelimination
943	Relation among three variables	Medium	systemssymmetry
949	Coupled linear conditions	Medium	simultaneous equationssymmetry
956	Proportion radical identity	Medium	proportionsratios
957	Continued proportion identity I	Medium	continued proportionratios
958	Continued proportion identity II	Medium	continued proportionratios
959	Continued proportion identity III	Medium	continued proportionalgebraic identity
960	Mean proportional algebraic relation	Medium	mean proportionalexponents
961	Product proportion identity	Medium	proportionscomponendo and dividendo
962	Solve rational equation	Medium	Rational equationsFactorisation
963	Solve quartic rational equation	Medium	Rational equationsFactorisation
964	Solve linear fractional equation	Medium	Cross‑multiplicationLinear equations
967	Work‑men‑days proportion problem	Medium	ProportionWork problems
1180	Rationalizing a Complex Quotient	Medium	rationalizationsurds
1199	Product involving cube roots	Medium	Cube roots of unityPeriodicity of powers of omega
1200	Power of binomials with omega	Medium	Cube roots of unityAlgebraic simplification
1202	Sum of cubes factorization	Medium	Cube roots of unityPolynomial factorization
1293	Radical Equation Solution	Medium	Algebraic manipulationRadical equations
1296	Fractional Radical Equation	Medium	Cross-multiplicationRadical equations
1297	Complex Radical Equation	Medium	Radical equationsSubstitution
1300	Reciprocal Fractions Equation	Medium	Reciprocal substitutionAlgebraic simplification
1370	Dividing 136 with Remainders	Medium	Diophantine equationsremainders
1371	Purchasing Three Types of Animals	Medium	Diophantine equationsword problems
1372	Coins in a Pocket	Medium	Diophantine equationscurrency word problem
1429	Binomial coefficient sum relation	Medium	Binomial TheoremCombinatorial Identities
1431	Weighted sum of binomial coefficients	Medium	Binomial TheoremIntegration
1432	Sum of squared binomial coefficients	Medium	Binomial TheoremVandermonde's Identity
1498	Coefficient Periodic Pattern	Medium	Generating FunctionsPower Series
1499	Factorial Series Identity for Even n	Medium	Binomial CoefficientsCombinatorial Identities
1514	Symmetric combinations of variables with omega (part 1)	Medium	Cube roots of unityAlgebraic identity
1515	Symmetric combinations of variables with omega (part 2)	Medium	Cube roots of unityAlgebraic identity
1516	Symmetric combinations of variables with omega (part 3)	Medium	Cube roots of unityAlgebraic identity
1531	Alternating Binomial Coefficient Identity	Medium	Binomial TheoremCoefficient Extraction
1532	Weighted Alternating Binomial Sum	Medium	Binomial TheoremDifferentiation

From open sources

193

Complete problems only, with worked solutions first. Show everything

#	Title	Difficulty
109557	Solve Equations Using Integers; The Division Property of Equality · Exercise 65	Medium
109559	Solve Equations Using Integers; The Division Property of Equality · Exercise 67	Medium
108838	Solving Equations Using the Subtraction and Addition Properties of Equality · Exercise 63	Medium
108840	Solving Equations Using the Subtraction and Addition Properties of Equality · Exercise 65	Medium
109555	Solve Equations Using Integers; The Division Property of Equality · Exercise 63	Medium
109565	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 75	Medium
109567	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 77	Medium
109569	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 79	Medium
109572	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 83	Medium
109573	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 85	Medium
109575	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 87	Medium
109577	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 89	Medium
109579	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 91	Medium
109581	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 93	Medium
109583	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 95	Medium
109585	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 97	Medium
109587	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 99	Medium
109589	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 101	Medium
109591	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 103	Medium
109593	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 105	Medium
109595	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 107	Medium
109597	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 109	Medium
109599	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 111	Medium
109601	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 113	Medium
109603	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 115	Medium
109605	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 117	Medium
109607	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 119	Medium
109609	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 121	Medium
109611	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 123	Medium
109613	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 125	Medium
109615	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 127	Medium
109617	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 129	Medium
109619	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 131	Medium
109621	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 133	Medium
109623	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 135	Medium
109625	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 137	Medium
109631	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 143	Medium
109633	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 145	Medium
109635	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 147	Medium
109637	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 149	Medium
109639	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 151	Medium
109641	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 153	Medium
109643	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 155	Medium
109645	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 157	Medium
109647	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 159	Medium
109649	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 161	Medium
109651	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 163	Medium
109653	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 165	Medium
109655	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 167	Medium
109657	Solve Equations Using Integers; The Division Property of Equality · Review Exercise 169	Medium