Solving equations with one unknown: FAQ

In an equation with variables on both sides, the unknown quantity (usually represented by a letter such as $x$‍) appears on both the left and right sides of the equation. To solve this type of equation, we usually try to isolate the variable on one side by manipulating the equation until we have only one instance of the variable.

For example, in the equation $2x+3=x+7$‍, we can subtract $x$‍ from both sides to isolate the variable on the left side: $x+3=7$‍. Then we can subtract $3$‍ from both sides to find that $x=4$‍.

Parentheses can be used in equations to group terms together. To solve an equation that contains parentheses, we usually use the distributive property to simplify the equation. For example, in the equation $2(x+4)=10$‍, we can distribute the $2$‍ to both $x$‍ and $4$‍ to get rid of the parentheses: $2x+8=10$‍.

There are a few things we can look at to determine the number of solutions an equation has. If we can simplify an equation down to a true statement with no variables (such as $5=5$‍), the equation has infinitely many solutions. If we simplify an equation down to an untrue statement with no variables (such as $5=6$‍), the equation has no solutions.

When it comes to word problems, we usually have to take a few extra steps to set up the equation before we can solve it. We start by identifying the unknown quantity and assigning it a variable. Then we translate the problem into an equation, using the information given in the word problem. Once we have the equation, we solve it as we would any other equation.

Solving equations comes in handy in a variety of real-world applications. For example, we might use an equation to figure out how much of a certain ingredient we need in a recipe, or to determine the number of hours we need to work to earn a certain amount of money. The ability to manipulate equations and solve for unknown quantities can be useful in countless situations.