Example

Example: Solving and Graphing 8x2(5x)<4(x+9)+6x8x - 2(5 - x) < 4(x + 9) + 6x

To solve the inequality 8x2(5x)<4(x+9)+6x8x - 2(5 - x) < 4(x + 9) + 6x, begin faithfully by simplifying each side. Proper distribution rapidly produces 8x10+2x<4x+36+6x8x - 10 + 2x < 4x + 36 + 6x. Consolidating like terms correctly cuts this parameter down to 10x10<10x+3610x - 10 < 10x + 36. Subtracting 10x10x from both sides abruptly eliminates the variable entirely, producing the final numerical statement 10<36-10 < 36. Because this represents a mathematically true statement unconditionally, the inequality formally operates as an identity, signifying that its valid solution strictly comprises all real numbers. On a typical number line, this graphically involves shading the line altogether. In functional interval notation, this definitive solution is visibly transcribed as (,)(-\infty, \infty).

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Updated 2026-04-22

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