Equation Solving: – Solving linear equations with one or two steps.

EQUATION SOLVING Solving linear equations with one or two steps. Grade 7 Mathematics: Equation Solving – Solving Linear Equations with One or Two Steps Subtopic Navigator Introduction Understanding Linear Equations Solving One-Step Equations Solving Two-Step Equations Checking Solutions Applications and Mixed Problems Cumulative Exercises Conclusion Lesson Objectives Define and recognize linear equations. Solve one-step linear equations using inverse operations. Solve two-step linear equations systematically. Verify solutions by substitution. Lesson Introduction An equation is a mathematical statement that shows two expressions are equal. A linear equation is an equation where the variable has a power of one. Solving an equation means finding the value of the variable that makes the statement true. For example: [latex]2x + 3 = 7[/latex]. Solving equations is like balancing a scale – whatever you do to one side, you must do to the other. Understanding Linear Equations A linear equation has the general form [latex]ax + b = c[/latex]. The goal is to isolate [latex]x[/latex] (the unknown) by applying inverse operations. Example 1: Is [latex]3x + 2 = 11[/latex] a linear equation? Solution: Yes. The variable [latex]x[/latex] has power 1, and the equation can be simplified to find [latex]x[/latex]. Example 2: Which of the following are linear equations? (a) [latex]2x - 5 = 9[/latex] (b) [latex]y^2 + 3 = 7[/latex] (c) [latex]4m = 20[/latex] Solution: (a) Linear, (b) Not linear (power of 2), (c) Linear. Exercises (Understanding Linear Equations) State whether [latex]5x + 7 = 0[/latex] is linear or not. Identify the variable in [latex]10y - 3 = 2[/latex]. Solving One-Step Equations One-step equations require only one operation (addition, subtraction, multiplication, or division) to isolate the variable. Example 3: Solve [latex]x + 7 = 12[/latex]. Solution: Subtract 7 from both sides: [latex]x = 12 - 7 = 5[/latex]. Example 4: Solve [latex]3y = 18[/latex]. Solution: Divide both sides by 3: [latex]y = 6[/latex]. Exercises (One-Step Equations) Solve [latex]x - 9 = 4[/latex]. Solve [latex]5m = 25[/latex]. Solving Two-Step Equations Two-step equations require two operations to isolate the variable. Always undo addition or subtraction first, then multiplication or division. Example 5: Solve [latex]2x + 5 = 13[/latex]. Solution: Subtract 5: [latex]2x = 8[/latex]. Divide by 2: [latex]x = 4[/latex]. Example 6: Solve [latex]4x - 3 = 9[/latex]. Solution: Add 3: [latex]4x = 12[/latex]. Divide by 4: [latex]x = 3[/latex]. Exercises (Two-Step Equations) Solve [latex]3x + 7 = 19[/latex]. Solve [latex]5y - 4 = 11[/latex]. Checking Solutions Always check your answer by substituting it back into the original equation. Example 7: Solve [latex]x + 6 = 10[/latex] and check. Solution: [latex]x = 4[/latex]. Substituting: [latex]4 + 6 = 10[/latex] ✔. Example 8: Solve [latex]2y - 1 = 7[/latex] and check. Solution: [latex]2y = 8 implies y = 4[/latex]. Check: [latex]2(4) - 1 = 7[/latex] ✔. Exercises (Checking Solutions) Solve and check: [latex]3x - 2 = 7[/latex]. Solve and check: [latex]m + 9 = 15[/latex]. Applications and Mixed Problems Example 9: A number increased by 7 is 15. Find the number. Solution: Let the number be [latex]x[/latex]. Equation: [latex]x + 7 = 15[/latex]. Solve: [latex]x = 8[/latex]. Example 10: If [latex]5y - 2 = 13[/latex], find [latex]y[/latex]. Solution: Add 2: [latex]5y = 15[/latex]. Divide: [latex]y = 3[/latex]. Exercises (Applications) The sum of a number and 12 is 25. Find the number. If twice a number minus 5 equals 11, find the number. Cumulative Exercises Solve [latex]x + 4 = 10[/latex]. Solve [latex]7y = 21[/latex]. Solve [latex]3m + 2 = 11[/latex]. Solve [latex]5x - 7 = 18[/latex]. Solve and check [latex]2p + 6 = 14[/latex]. The sum of a number and 15 is 30. Find the number. If [latex]4n - 5 = 11[/latex], find [latex]n[/latex]. Solve [latex]9 + x = 20[/latex]. Solve [latex]10y - 2 = 28[/latex]. A number divided by 3 equals 7. Find the number. Conclusion/Recap In this lesson, we learned how to solve one-step and two-step linear equations by applying inverse operations. We also practiced checking solutions and solving application-based problems. Mastering linear equations is essential because they form the basis of algebra and appear frequently in exams. Clip It! Share your ANSWER in the Chat. Indicate TITLE e.g Linear Equation 1. .....2. e.t.c