diff --git a/README.md b/README.md
index 2752819..0c1868f 100644
--- a/README.md
+++ b/README.md
@@ -7,7 +7,7 @@ A graphing calculator written in C++ with an ImGui user interface rendered with
 ## How to get started
 
 The codebase of this repo is quite big, but the file that is of interest to you as a contributor is [
-`src/code/Core/Application.cpp`](src/core/Core/Application.cpp). It contains the code for parsing expressions 
+`src/core/Core/Application.cpp`](src/core/Core/Application.cpp). It contains the code for parsing expressions 
 (using [ExprTk](https://github.com/ArashPartow/exprtk)) and the rendering logic for calculating the graph's points. Most,
 if not all features can be implemented by only modifying this one file.
 
diff --git a/src/core/Core/Application.cpp b/src/core/Core/Application.cpp
index 23764d9..aab4c77 100644
--- a/src/core/Core/Application.cpp
+++ b/src/core/Core/Application.cpp
@@ -212,18 +212,88 @@ ExitStatus App::Application::run() {
           }
         }
 
-        // check for implicit form: f(x,y) = g(x,y)
-        if (!plotted) {
-          size_t equals_pos = findTopLevelEquals(func_str);
+        // check for inequality 
+        if (!plotted && hasInequalityOperator(func_str)) {
+          double x = 0.0, y = 0.0;
+          exprtk::symbol_table<double> symbol_table;
+          symbol_table.add_constants();
+          addConstants(symbol_table);
+          symbol_table.add_variable("x", x);
+          symbol_table.add_variable("y", y);
+          
+          exprtk::expression<double> expression;
+          expression.register_symbol_table(symbol_table);
+          
+          exprtk::parser<double> parser;
           
-          if (equals_pos != std::string::npos) {
-            // split into LHS and RHS
-            std::string lhs = trim(func_str.substr(0, equals_pos));
-            std::string rhs = trim(func_str.substr(equals_pos + 1));
+          if (parser.compile(func_str, expression)) {
+            // grid parameters
+            const double x_min = -canvas_sz.x / (2 * zoom);
+            const double x_max = canvas_sz.x / (2 * zoom);
+            const double y_min = -canvas_sz.y / (2 * zoom);
+            const double y_max = canvas_sz.y / (2 * zoom);
             
-            // create expression: LHS - RHS
-            std::string implicit_expr = "(" + lhs + ") - (" + rhs + ")";
+            // adaptive step size with performance limit
+            const double step = std::max(0.025, 1.5 / zoom);
+            const ImU32 inequality_color = IM_COL32(100, 150, 255, 180);
+            const float dot_size = std::max(1.5f, zoom / 60.0f);
             
+            
+            for (y = y_min; y <= y_max; y += step) {
+              for (x = x_min; x <= x_max; x += step) {
+                
+                // if expression is true, plot the point
+                if (expression.value() == 1.0) {
+                  ImVec2 screen_pos(origin.x + static_cast<float>(x * zoom),
+                                   origin.y - static_cast<float>(y * zoom));
+                  draw_list->AddCircleFilled(screen_pos, dot_size, inequality_color);
+                }
+              }
+            }
+            
+            plotted = true;
+          }
+        }
+
+        // check for implicit form: f(x,y) = g(x,y)
+        if (!plotted) {
+          size_t equals_pos = findTopLevelEquals(func_str);      
+          bool has_double_equals = hasEqualsEqualsOperator(func_str);
+
+          if (equals_pos != std::string::npos || has_double_equals) {
+          
+            std::string implicit_expr;
+
+            if (has_double_equals) {
+              // Handle == operator
+              std::string temp_str = func_str;
+              int depth = 0;
+              size_t eq_pos = std::string::npos;
+              
+              for (size_t i = 0; i < temp_str.size() - 1; ++i) {
+                char c = temp_str[i];
+                if (c == '(') ++depth;
+                else if (c == ')') --depth;
+                else if (depth == 0 && c == '=' && temp_str[i+1] == '=') {
+                  eq_pos = i;
+                  break;
+                }
+              }
+              
+              if (eq_pos != std::string::npos) {
+                std::string lhs = trim(temp_str.substr(0, eq_pos));
+                std::string rhs = trim(temp_str.substr(eq_pos + 2)); // +2 to skip ==
+                implicit_expr = "(" + lhs + ") - (" + rhs + ")";
+              }
+            } else {
+              // Handle = operator
+              std::string lhs = trim(func_str.substr(0, equals_pos));
+              std::string rhs = trim(func_str.substr(equals_pos + 1));
+              implicit_expr = "(" + lhs + ") - (" + rhs + ")";
+            }
+
+            if (!implicit_expr.empty()) {
+              
             // setup exprtk with x and y variables
             double x = 0.0, y = 0.0;
             exprtk::symbol_table<double> symbolTable;
@@ -298,7 +368,8 @@ ExitStatus App::Application::run() {
                 }
               }
               
-              plotted = true;
+                plotted = true;
+              }
             }
           }
         }
diff --git a/src/core/Core/funcs.hpp b/src/core/Core/funcs.hpp
index d945fc5..128f6b4 100644
--- a/src/core/Core/funcs.hpp
+++ b/src/core/Core/funcs.hpp
@@ -56,5 +56,47 @@ static size_t findTopLevelEquals(const std::string& str) {
   return std::string::npos;
 }
 
+//function to check for == operator specifically
+static bool hasEqualsEqualsOperator(const std::string& str) {
+  int depth = 0;
+  for (size_t i = 0; i < str.size(); ++i) {
+    char c = str[i];
+    
+    if (c == '(') {
+      ++depth;
+    } else if (c == ')') {
+      --depth;
+    } else if (depth == 0) {
+      if (c == '=' && i + 1 < str.size() && str[i+1] == '=') {
+        return true;
+      }
+    }
+  }
+  return false;
+}
+
+// function to check if expression contains inequality operators
+static bool hasInequalityOperator(const std::string& str) {
+  int depth = 0;
+  for (size_t i = 0; i < str.size(); ++i) {
+    char c = str[i];
+    
+    if (c == '(') {
+      ++depth;
+    } else if (c == ')') {
+      --depth;
+    } else if (depth == 0) {
+      // check for <, >, <=, >=, !=
+      if (c == '<' || c == '>') {
+        return true;
+      }
+      if (c == '!' && i + 1 < str.size() && str[i+1] == '=') {
+        return true;
+      }
+    }
+  }
+  return false;
+}
+
 #endif  // IMGRAPH_FUNCS_HPP