Solving Word Problems with Linear Equations: A Simple Guide

Let's learn how to break down word problems with Spark.E!Here's a sample problem we'll use to demonstrate our approach.The first step is to read the problem carefully, making sure we understand what's being asked.Next, we identify the key information in the problem.We need to note the relationship between Sarah and her brother's ages.And clearly identify what we're trying to find.The third step is to list all known values.Finally, we define our variable. In this case, let's use x to represent the brother's age.Here are some helpful tips for organizing your work when breaking down word problems.Now that we've broken down the problem and identified our variable, we're ready for the next step.To convert word problems into equations, we need to understand common mathematical phrases and their symbols.Let's practice with this example: A number increased by 5 is three times the same number decreased by 2.First, we define our variable. Let x represent the unknown number.For the left side, 'increased by 5' means we add 5 to our number x.On the right side, we first write x minus 2 for 'decreased by 2', then multiply by 3 for 'three times'.Putting it all together, we get x plus 5 equals 3 times the quantity x minus 2.When converting word problems to equations, watch out for these common mistakes.Be careful not to reverse inequality signs, forget parentheses, mix up the order of operations, or omit multiplication signs.Now it's your turn! Try converting this word problem into an equation: Six more than twice a number equals the number plus ten.The equation should be: two x plus six equals x plus ten. Notice how we converted 'twice a number' to two x, and 'six more than' became plus six.Let's solve this equation step by step and verify our answer.We start with the equation x plus two x equals thirty-six.First, let's combine like terms. X plus two x gives us three x.Now we can solve for x by dividing both sides by three.Let's verify our answer by plugging twelve back into the original equation.We start with x plus two x equals thirty-six.Replace x with twelve.Twelve plus two times twelve.Twelve plus twenty-four.Which equals thirty-six. Our answer checks out!Therefore, we can confidently state that the number we're looking for is twelve.Remember to always verify your answer by plugging it back into the original equation.