tabulate( function() { return randRange( 2, 9 ) * ( rand( 3 ) > 0 ? 1 : -1 ); } , 2 ) tabulate( function(i) { return fraction( 1, COEF[i] ); }, 2 ) randFromArray( [ "-", "+" ], 2) tabulate( function() { return rand( 3 ) > 0 ? randRange( 2, 9 ) : 0; }, 2 ) tabulate( function(i) { return LEFT_INT[i] * ( SIGN[i] === "+" ? -1 : 1 ); }, 2 ) randFromArray( [ "<", ">", "≤", "≥" ], 2 ) tabulate( function(i) { return randRange( 1, 6 ) * abs( COEF[i] ) + ( SIGN[i] === "+" ? 1 : -1 ) * LEFT_INT[i]; }, 2 ) randFromArray([ "a", "b", "c", "x", "y", "z" ]) tabulate( function(i) { return getComp( COEF[i], COMP[i] ); }, 2 ) tabulate( function(i) { return fraction( RIGHT_INT[i] + ADD_TO_SIMPLIFY[i], COEF[i] ); }, 2 ) tabulate( function(i) { return ( RIGHT_INT[i] + ADD_TO_SIMPLIFY[i] ) / COEF[i]; }, 2 ) [ "first", "second" ] [ "#1F78B4", "#B30000" ] tabulate( function(i) { return COMP_SOLUTION[i] === "≤" || COMP_SOLUTION[i] === "≥"; }, 2 ) tabulate( function(i) { return COMP_SOLUTION[i] === "≤" || COMP_SOLUTION[i] === "<"; }, 2 ) ( LESS_THAN[0] && !LESS_THAN[1] && SOLUTION[0] >= SOLUTION [1] ) || ( !LESS_THAN[0] && LESS_THAN[1] && SOLUTION[0] <= SOLUTION [1] ) ( LESS_THAN[0] && !LESS_THAN[1] && SOLUTION[1] > SOLUTION[0] ) || ( !LESS_THAN[0] && LESS_THAN[1] && SOLUTION[0] > SOLUTION[1] ) || ( LESS_THAN[0] !== LESS_THAN[1] && SOLUTION[0] === SOLUTION[1] && ( !INCLUSIVE[0] || !INCLUSIVE[1] ) ) randFromArray([ "or", "and" ]) OR === "or" tabulate( function() { return randRange( 2, 9 ) * ( rand( 3 ) > 0 ? 1 : -1 ); }, 2 ) (function() { if ( LESS_THAN[0] && LESS_THAN[1] ) { if ( SOLUTION[0] === SOLUTION[1] ) { return INCLUSIVE[0] ? 1 : 2; } return SOLUTION[0] > SOLUTION[1] ? 1 : 2; } else if ( !LESS_THAN[0] && !LESS_THAN[1] ) { if ( SOLUTION[0] === SOLUTION[1] ) { return INCLUSIVE[0] ? 1 : 2; } return SOLUTION[0] < SOLUTION[1] ? 1 : 2; } return 0; })() CONTAINS === 1 ? 2 : 1 SOLUTION[0] === SOLUTION[1] && INCLUSIVE[0] && INCLUSIVE[1] && ( LESS_THAN[0] ? !LESS_THAN[1] : LESS_THAN[0] )

Solve for VARIABLE_NAME:

\color{COLOR[0]}{COEF[0] + VARIABLE_NAMESIGN[0] + LEFT_INT[0]COMP[0] + RIGHT_INT[0]} OR \color{COLOR[1]}{COEF[1] + VARIABLE_NAMESIGN[1] + LEFT_INT[1]COMP[1] + RIGHT_INT[1]}

VARIABLE_NAME = SOLUTION[0] All real numbers. VARIABLE_NAME + COMP_SOLUTION[CONTAINS - 1] + SOLUTION[CONTAINS - 1] VARIABLE_NAME + COMP_SOLUTION[IS_CONTAINED - 1] + SOLUTION[IS_CONTAINED - 1] No solution. VARIABLE_NAME + COMP_SOLUTION[0] + SOLUTION[0] OR VARIABLE_NAME + COMP_SOLUTION[1] + SOLUTION[1]

  • VARIABLE_NAME + COMP_SOLUTION[0] + FAKE_ANSWER[0] OR VARIABLE_NAME + COMP_SOLUTION[1] + FAKE_ANSWER[1]
  • VARIABLE_NAME + COMP_SOLUTION[0] + SOLUTION[0] OR VARIABLE_NAME + COMP_SOLUTION[1] + randRangeNonZero( -9, 9 )
  • VARIABLE_NAME + COMP_SOLUTION[0] + randRangeNonZero( -9, 9 ) OR VARIABLE_NAME + COMP_SOLUTION[1] + SOLUTION[1]
  • VARIABLE_NAME + COMP_SOLUTION[0] + FAKE_ANSWER[0]
  • VARIABLE_NAME + COMP_SOLUTION[0] + SOLUTION[0] OR VARIABLE_NAME + COMP_SOLUTION[1] + SOLUTION[1]
  • VARIABLE_NAME + COMP[0] + SOLUTION[0] OR VARIABLE_NAME + COMP_SOLUTION[1] + SOLUTION[1]
  • VARIABLE_NAME + COMP[0] + FAKE_ANSWER[0] OR VARIABLE_NAME + COMP_SOLUTION[1] + FAKE_ANSWER[1]
  • VARIABLE_NAME + COMP_SOLUTION[0] + SOLUTION[0] OR VARIABLE_NAME + COMP[1] + SOLUTION[1]
  • VARIABLE_NAME + COMP_SOLUTION[0] + FAKE_ANSWER[0] OR VARIABLE_NAME + COMP[1] + FAKE_ANSWER[1]
  • VARIABLE_NAME + COMP[0] + SOLUTION[0] OR VARIABLE_NAME + COMP[1] + SOLUTION[1]
  • VARIABLE_NAME + COMP[0] + FAKE_ANSWER[0] OR VARIABLE_NAME + COMP[1] + FAKE_ANSWER[1]
  • VARIABLE_NAME + COMP_SOLUTION[0] + round( ( RIGHT_INT[0] - ADD_TO_SIMPLIFY[0] ) / COEF[0] ) OR VARIABLE_NAME + COMP_SOLUTION[1] + round( ( RIGHT_INT[1] - ADD_TO_SIMPLIFY[1] ) / COEF[1] )
  • All real numbers.
  • No solution.
  • VARIABLE_NAME = SOLUTION[0]

The FIRST[i] inequality can be simplified into this:

\color{COLOR[i]}{VARIABLE_NAME + COMP_SOLUTION[i] + SOLUTION[i]}

var start = min( SOLUTION[0], SOLUTION[1] ) - randRange( 2, 5 ); var end = max( SOLUTION[0], SOLUTION[1] ) + randRange( 2, 5 ); init({ range: [ [ start - 1, end + 1 ], [ -1, 1 ] ], scale: 28 }); numberLine( start, end, null, start ); // Draw both inequalities var y_placement = [ 0.05, -0.05 ]; for ( var i = 0; i < 2; i++ ) { style({ stroke: COLOR[i], fill: COLOR[i], strokeWidth: 3.5, arrows: "->" }); path([ [ SOLUTION[i] + 0.15 * ( LESS_THAN[i] ? -1 : 1 ), y_placement[i] ], [ LESS_THAN[i] ? start : end, y_placement[i] ] ]); style({ stroke: COLOR[i], fill: INCLUSIVE[i] ? COLOR[i] : null }); circle( [ SOLUTION[i], y_placement[i] ], 0.2 ); }

Since this is an "or" inequality, the solution is the part of the number line which is covered by either of the graphs of the inequalities.

The combined graphs of the inequalities span the entire number line, therefore the solution is "All real numbers."

Notice how the FIRST[IS_CONTAINED - 1] inequality is completely included by the FIRST[CONTAINS - 1] inequality. Therefore the answer is:

\color{COLOR[CONTAINS - 1]}{VARIABLE_NAME + COMP_SOLUTION[CONTAINS - 1] + SOLUTION[CONTAINS - 1]}

Therefore, since the graphs of the equalities do not intersect, the solution is:

\color{COLOR[0]}{VARIABLE_NAME + COMP_SOLUTION[0] + SOLUTION[0]} or \color{COLOR[1]}{VARIABLE_NAME + COMP_SOLUTION[1] + SOLUTION[1]}

The solution to an inequality with the word "and" is the intersection of the graphs of the inequalities.

Therefore, the solution is:

\color{magenta}{VARIABLE_NAME = SOLUTION[0]}

Since the graphs of the inequalities do not intersect, there is no solution.

Since the FIRST[IS_CONTAINED - 1] inequality is completely included by the FIRST[CONTAINS - 1] inequality, their intersection is the FIRST[IS_CONTAINED -1] inequality. Therefore the answer is:

\color{COLOR[IS_CONTAINED - 1]}{VARIABLE_NAME + COMP_SOLUTION[IS_CONTAINED - 1] + SOLUTION[IS_CONTAINED - 1]}

Therefore, the solution is:

\color{COLOR[0]}{VARIABLE_NAME + COMP_SOLUTION[0] + SOLUTION[0]} and \color{COLOR[1]}{VARIABLE_NAME + COMP_SOLUTION[1] + SOLUTION[1]}