Solving Linear Equations. Finding the Unknown. IntroductionSolving Linear equations is a fundamental skill in algebra that involves finding the value of an unknown variable. It's like playing a detective game, where you use clues and logical reasoning to uncover the hidden value. In this article, we'll explore different types of equations and the strategies used to solve them.Linear EquationsLinear equations are equations where the highest power of the variable is 1. A linear equation is an equation that can be written in the form Ax + B = C, where A, B, and C are constants and x is the variable. They can be solved by isolating the variable on one side of the equation.Example 1Solve the equation [latex]2x + 5 = 13[/latex].[latex]2x = 13-5[/latex].[latex]2x = 8[/latex].[latex]frac{2x}{2} = frac{8}{2}[/latex].[latex]x = 4[/latex].Example 2The sum of the ages of a grandfather, father, and son is 130. The grandfather is twice as old as the father. The father is 10 years older than the son. Find the age of each.Let the son's age be x.Then, the father's age is x + 10.And the grandfather's age is 2(x + 10). The sum of their ages is 130, so:[latex] x + (x + 10) + 2(x + 10) = 130[/latex] [latex]4x + 30 = 130[/latex] [latex]4x = 100[/latex] [latex]x = 25[/latex] Son's age: [latex]x = 25[/latex] Father's age: [latex]x + 10 = 25 + 10 = 35[/latex] Grandfather's age: [latex]2(x + 10) = 2(25 + 10) = 2(35) = 70[/latex] Therefore, the son is 25 years old, the father is 35 years old, and the grandfather is 70 years old. Strategies for Solving Linear EquationsIsolate the variable: Get the variable alone on one side of the equation.Combine like terms: Simplify the equation by combining similar terms.Use inverse operations: Perform the opposite operation to undo the given operation.Check your solution: Substitute the solution back into the original equation to verify that it makes the equation true.ConclusionSolving Linear equations is a fundamental skill in algebra that involves applying logical reasoning and algebraic techniques. By mastering various methods for solving equations, you can tackle complex problems and succeed in mathematics.EXERCISE 13.0.[latex]3(x + 2)-4 = 11[/latex][latex]frac{2}{3x}-5 = 1[/latex]0.4x + 1.2 = 3.6[latex]frac{1}{2x} + frac{3}{4} = frac{5}{8}[/latex][latex]-3x + 7 = 16[/latex][latex]2x + 3 = 2x + 5[/latex][latex]2x + 4 = 2(x + 2)[/latex][latex]frac{3}{x + 2} = 1[/latex]The sum of the ages of a father and his son is 45. If the father is 15 years older than his son, how old is each of them?A train travels at a constant speed of 60 miles per hour. How long will it take to travel 300 miles?A taxi charges a flat fee of N3.00 plus N0.50 per mile. If a ride costs N10.50, how many miles was the ride?A chemist has 20 liters of a 30% acid solution. How many liters of pure acid must be added to obtain a 40% acid solution?A company sells a product for N25 per unit. The cost to produce x units is given by C(x) = 15x + 1000. How many units must the company sell to break even?Simplify the fraction [latex]frac{x^{2} - 4}{ x + 2}[/latex]Add the fractions [latex]frac{x + 1}{x - 2}[/latex] and [latex]frac{x - 3}{x + 2}[/latex]Submit Answers via Chat e.g Exercise 13.o, then type Answers (Number your Answers).FOR MORE CONTENT!!!Register HERE Now! Pick a course, watch our Videos and take our CBT's.Additional Resources:N/A: https://www.waokmath.com[Image Source]: https://www.freepik.com/.
