Solving 3x + 5 = x + 13

Pre-Algebra · Axiom Academy

EXAMPLE Variables on Both Sides Solve 3x + 5 = x + 13 by deciding which way to move the x terms, then isolating x . Solve the equation 3x + 5 = x + 13 . Here the variable shows up on both sides, so before we can isolate x we first have to gather every x term onto one side. You get to decide which side. Nice work. You solved an equation with the variable on both sides by gathering the x terms first, then isolating x . Gather first: when x appears on both sides, move all x terms to one side before isolating. Your choice of side: subtracting x keeps the coefficient positive ( 2x = 8 ); subtracting 3x instead gives -2x = -8 . Both routes reach the same answer. Result: , and substituting back gives 17 = 17 . Pick whichever side feels easier — the equality stays true as long as you do the same operation to both sides every step.

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