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Equation tool guide

Write the next line:
Step 1 of 11
  • The first line is the exercise; each line under it is the equation after one more step.
  • = goes on to the right side: each side is a card of its own.
  • Enter checks the line and opens the next one.
  • ✓ – the line has the same solutions as the line before it.
  • The box at the end of a line holds what you did to both sides: −3\displaystyle -3, :2\displaystyle :2.
  • It is for you and for the teacher: the tool does not check it.
  • The solution is done when the unknown stands alone on one side and a number on the other.
  • Then the tool says “Correct ✓”.
  • 2x=14\displaystyle {2x}={14} does not have the solution of the line before, so the tool marks it with “!”.
  • The words under the line say what went wrong, never the answer.
  • × deletes a line.
  • A product is 0 when one of its factors is 0.
  • So the next line has two equations, joined by “or”.
  • ⌫ in an empty equation takes it away.
  • The quadratic formula: x1,2=−b±b2−4ac2a\displaystyle {x_{1,2}}={\frac{-b\pm\sqrt{b^2-4ac}}{2a}}
  • Line 2 puts into it a=1\displaystyle {a}={1}, b=−4\displaystyle {b}={-4}, c=1\displaystyle {c}={1} from x2−4x+1=0\displaystyle {x^2-4x+1}={0}.
  • ± writes both solutions in one line: 2+3\displaystyle 2+\sqrt3 and 2−3\displaystyle 2-\sqrt3.
  • The tool checks lines with roots too: 12=23\displaystyle {\sqrt{12}}={2\sqrt3}.
  • The solution is done when the root cannot be simplified any further.
  • < and > go on to the right side with that sign.
  • = right after them makes ≤\displaystyle \le or ≥\displaystyle \ge.
  • A new line starts with the sign of the line above it.
  • Dividing both sides by a negative number turns the sign around: −2x>6\displaystyle -2x>6 becomes x<−3\displaystyle x<-3.
  • The sign is a button: its menu has =\displaystyle {}={}, <\displaystyle <, >\displaystyle >, ≤\displaystyle \le, ≥\displaystyle \ge.
  • A square is never negative, so no number solves x2=−4\displaystyle {x^2}={-4}.
  • ∅ says there is no solution.
  • “every x” beside it says that every number is a solution.
  • −2<x≤3\displaystyle -2<x\le3 is two inequalities at once: x\displaystyle x is between −2\displaystyle -2 and 3\displaystyle 3.
  • <\displaystyle < in the right card adds a second sign and a third card.
  • The button a<x<b does the same.
  • A system is two equations together: its solution is a pair x\displaystyle x, y\displaystyle y that solves both.
  • The brace joins the equations of a line: each must be true.
  • Line 2 puts x+2\displaystyle x+2 in place of y\displaystyle y in the second equation: an equation with x\displaystyle x alone.
  • From it x=5\displaystyle {x}={5}, and then y=5+2=7\displaystyle {y}={5+2}={7}.
  • The solution is done when each unknown stands alone with a number.