Algebra, averages & word problems · Topic 9 of 15

Basic Algebra: Expressions & Solving for x

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Math · algebra

Evaluate by substituting and following the order of operations; solve by undoing each operation on both sides until x stands alone.

01 · Solve for xSame operation on both sides isolates x

02 · Two-step equationsTwo-step: undo + or − first, then × or ÷

03 · EvaluateEvaluate: plug in, then order of operations

Variable = a letter for an unknown number; constant = a fixed number must know

Coefficient = the number in front of the variable (x means 1x)

Expression: no equal sign. Equation: has an equal sign

Do the same thing to both sides to isolate x must know

Two-step: undo + or − first, then × or ÷ must know

Evaluate: substitute the value, then use order of operations must know

Check: put the answer back in; both sides must match

Combine like terms by adding coefficients: 3x + 5x = 8x

Side by side means multiply: 4x = 4 × x

Fraction × x? Multiply both sides by the reciprocal: (3/4)x = 12 → 16

Distribute first: 2(x + 3) = 18 → 2x + 6 = 18 → x = 6

Worked examples

6x = 42 → ÷ 6 → x = 7

Worked examples

3x + 5 = 26 → 3x = 21 → x = 7

2a² − 3b, a = 3, b = 4: 2(9) − 12 = 6

Commonly confused

Watch the sign: −4x = 20 → x = −5

Subtract before you divide: 3x + 5 = 26 is x = 7, not 21

Show 3 more facts

x on both sides: gather x terms on one side (5x − 4 = 2x + 11 → x = 5)

Simplify sides → collect x terms → collect numbers → coefficient 1 → check

(a + b)² = a² + 2ab + b² (beyond one- and two-step solving)

Pearl

Whatever you do to one side, do to the other.

Practice this topic, then test the whole section.

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