Linear Equation Solving Guide with Step-by-Step Process

This infographic is presented in English, titled "(Linear Equations in One Unknown: Complete Solving Process + Answer Analysis Guide)", using a clear grid layout divided into multiple rectangular modules, each enclosed by a thick black border with structured content inside. The overall style is simple and clear, using arrows, color coding (such as blue explanation boxes and red warning triangles), and symbols (such as √ and ×) to enhance readability and teaching effectiveness. The chart is divided into two main parts: the upper half shows the four-step solving process, and the lower half is a pitfall-avoidance guide to high-frequency mistakes. **Part 1: The Four-Step Solving Process** This part consists of four vertically arranged step modules (Step1 through Step4) plus an answer-verification module placed side by side on the right. - **Step1: Remove Parentheses** - Original equation: 3(x-2)+4=2x+1 - Operation: apply the distributive law of multiplication to expand the parentheses → 3x-6+4=2x+1 - Blue explanation box: "Use the distributive law of multiplication to expand all parentheses" - Red warning triangle tips: - "When the coefficient is negative, all terms inside the parentheses must change sign" - "Do not omit multiplying the constant term inside the parentheses" - **Step2: Move Terms** - Current equation: 3x-6+4=2x+1 - Operation: move the x-terms to the left side and the constant terms to the right side → 3x-2x=1+6-4 - Blue explanation box: "Terms change sign when moved; like terms sit on opposite sides of the equals sign" - Red warning triangle tip: "Moved terms must change their positive/negative sign" - Crossing arrows are used to visualize the term-moving process. - **Step3: Combine Like Terms** - Current equation: 3x-2x=1+6-4 - Operation: combine the x-terms on the left (3x-2x=x) and the constant terms on the right (1+6-4=3) → x=3 - Blue explanation box: "Add the coefficients of like terms, simplifying into the standard form ax=b" - Red warning triangle tip: "Pay attention to positive/negative sign arithmetic when combining constant terms" - **Step4: Make the Coefficient 1** - Current equation: x=3 - Operation: divide both sides of the equals sign by the coefficient of the unknown (here the coefficient is 1, so no action is needed) → x=3 - Blue explanation box: "Divide both sides of the equals sign by the coefficient of the unknown to obtain the value of x" - Supplementary note on the right: "If the coefficient is a fraction, you can multiply both sides by the reciprocal of the denominator to simplify the calculation" - A blue check mark "√" appears beside the result - **Answer Verification: Checking the Solution by Substitution** - Divided into left and right columns, separated by a dashed line in the middle. - Left column: computation of the left side of the original equation - Substituted value: x=3 - Computation: 3*(3-2)+4 → 3*1+4 → 3+4 → result 7 - Right column: computation of the right side of the original equation - Substituted value: x=3 - Computation: 2*3+1 → 6+1 → result 7 - Large blue text at the bottom: "7 = 7" - Blue check mark "√" + text: "Both sides are equal → the solution is correct" **Part 2: Pitfall-Avoidance Guide to High-Frequency Solving Mistakes** Located at the bottom, four sub-modules are arranged horizontally, each separated by dashed lines and beginning with a red warning triangle, indicating common error types: - **⚠️ Parenthesis Removal Errors** - Wrong example: 3(x-2) → 3x-2 ❌ (omitting the constant term or failing to flip signs) - Correct example: 3(x-2) → 3x-6 ✅ - **⚠️ Sign-Flipping Errors When Moving Terms** - Wrong example: 3x=2x+1 → 3x+2x=1 ❌ (sign not changed when moving the term) - Correct example: 3x=2x+1 → 3x-2x=1 ✅ - **⚠️ Like-Term Combination Errors** - Wrong examples: - 3x-2x → 5x ❌ - 1+6-4 → 11 ❌ - Correct examples: - 3x-2x → x ✅ - 1+6-4 → 3 ✅ - Text explanation below: "Errors in coefficient addition/subtraction" - **⚠️ Coefficient-to-1 Errors** - Correct example: - 2x=4 → x=4/2=2 ✅ - x/2=4 → x=4*2=8 ❌ (the original shows x=4/2=2, but logically it should be x=4×2=8; this is likely a typo or typesetting error in the image, and the actual intent is to point out the "divisor and dividend swapped" mistake) - The wrong example in the image reads: x/2=4 → x=4/2=2 ❌, which is mathematically incorrect; the correct answer should be x=8. - Text explanation below: "Divisor and dividend are swapped" Through step-by-step teaching, contrastive demonstration, warning tips, and final verification, the infographic systematically guides users to master the complete solving process for linear equations in one unknown and to effectively avoid common mistakes.