The most obvious way that algebra will help you as an adult is if you have any wish to attend college or pursue a career that requires the use of algebra. Different mathematics branches and sciences build on each other. You need an understanding of algebra to do calculus, chemistry or physics, for example. But you also need algebra in non-scientific fields such as architecture, engineering, construction and design. Without knowledge of algebra, even for professions not requiring a college degree, you will not be able to get jobs in these fields.
Algebra uses general equations to find answers to specific problems. When you practice algebra, as well as other types of math, you are training your brain to think logically and find solutions. This problem-solving skill translates to other areas of life, as well. When you can logically think through a situation and arrange the parts of the situation to lead you to a solution, both personal and work life become more manageable. Problem-solving is a skill many employers look for in an employee, even if the job requires no math.
Balancing a check book only requires basic addition and subtraction. But if you plan to buy a house or a car, get a credit card or have an interest-bearing account of any kind, algebra will give you the ability to figure out interest, payments, rates and the time it will take to pay back the principal. This can help you find the best deal when shopping for a loan or an investment. Even simple financial transactions like buying items at a discount or finding sales tax use algebra.
Keeping track of your vehicle's gas mileage when you fill up is algebraic task. If you are planning a party and need to know how many tables you can put in the room and how many people will have to be at each table, you can use algebra to simplify the process. Landscaping your yard and figuring out where to put the trees, staking off a rectangular area for a garden or determining how many fish your pond will hold are all tasks that you can use algebra for in your adult life.