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Learn to solve for a variable in a simple equation
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An equation is a mathematical sentence that expresses two equal values. [1] X Research source In algebra, you'll often work with equations that have an unknown value represented by a variable, or letter. To solve these equations, you need to find the value of the variable. A one-step equation is one in which you only have to perform just one operation to determine the unknown value, and so these type of equations are the easiest to solve. We'll show you how!
Things You Should Know
- Write down your equation and identify how to "isolate" the variable, to get it alone one side of the equals sign.
- Add or subtract the constant that's on the same side of the equals sign as the variable from both sides of the equation.
- Or, multiply or divide the constant if the equation uses multiplication or division.
Steps
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Write down the equation. It’s easy to solve equations when you understand what they mean. An equation will have a variable (usually ), which represents an unknown value. The equation will also have a constant, which is a number you need to add or subtract from the variable to equal a certain sum or difference.
- For example, you might have the equation . The variable representing the unknown number is . When you subtract 9 from the unknown number, the difference is 5.
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Determine how to isolate the variable. To isolate a variable, you need to get it alone on one side of the equation by performing an inverse operation to cancel the constants. Addition and subtraction are inverse operations. So, if the constant is subtracted in the equation, to cancel it you would add. [2] X Research source
- For example, in the equation , 9 is subtracted from the variable, so to isolate the variable you must cancel the 9 by adding it.
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Add or subtract the constant from both sides of the equation. As you manipulate equations to solve them, you must keep both sides balanced. Whatever you do to one side of the equation, you must do to the other side. So, if you need to add a value to isolate the variable, you must also add that same value to the other side of the equation. [3] X Research source
- For example, in the equation
, you need to add 9 to the left side to isolate the variable, so you also need to add 9 to the right side of the equation:
.
- For example, in the equation
, you need to add 9 to the left side to isolate the variable, so you also need to add 9 to the right side of the equation:
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Check your work. To make sure your solution is correct, plug the value of into the original equation. If the equation is true, your solution is correct. [4] X Research source
- For example, if you found that , substitute 14 for in the original equation: . Since this equation is true, your solution is correct.
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Evaluate the equation. The variable, usually , represents an unknown value. Solving an equation means finding the unknown value. The equation may also have a coefficient, which is a number you need to multiply by the variable to equal a certain product. The variable may also be the numerator of a fraction. This means you need to divide the variable by the number in the denominator to equal a certain quotient.
- For example, you might have the equation . The variable representing the unknown number is . When you multiply the unknown number and 3, the product is 24.
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Determine how to isolate the variable. Isolating a variable means getting it by itself on one side of the equation. To do this you must perform an inverse operation to cancel coefficients or fractions. Multiplication and division are inverse operations. If the variable has a coefficient, to cancel it you would divide by the coefficient, since any number divided by itself is equal to 1. If the variable is the numerator of a fraction, to isolate it you would multiply by the denominator, since multiplying by a number cancels the division by that number. [5] X Research source
- For example, in the equation the variable is multiplied by 3, so to isolate the variable you must cancel the 3 by dividing by 3.
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Multiply or divide from both sides of the equation. As you solve an equation the most important thing to remember is that you must keep both sides of the equation balanced. This means that whatever you do to one side of the equation, you must do to the other side, too. [6] X Research source So, if you need to divide by a value to isolate the variable, you must also divide by the same value on the other side of the equation. [7] X Research source
- For example, in the equation
, you need to divide by 3 on the left side to isolate the variable, so you also need to divide by 3 on the right side of the equation:
- For example, in the equation
, you need to divide by 3 on the left side to isolate the variable, so you also need to divide by 3 on the right side of the equation:
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Check your solution. To make sure your answer is correct, plug the value of into the original equation. If the equation is true, your solution is correct. [8] X Research source
- For example, if you found that , substitute 8 for in the original equation: . Since this equation is true, your solution is correct.
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Solve this equation with a fraction: .
- Since the variable is divided by 4, to isolate it you need to multiply by 4.
- Checking your work, since , your solution is correct.
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Solve this equation with a negative constant: .
- Since the constant is negative, adding it to both sides will isolate the variable.
- Checking your work, since , your solution is correct.
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Solve this equation with a negative coefficient: .
- Since the variable is multiplied by -5, to isolate the variable, you must divide each side by -5. Remember that dividing a positive number by a negative number equals a negative quotient.
- Checking your work, since , your solution is correct.
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Expert Q&A
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QuestionWhat is an extraneous solution in a rational equation?Jake Adams is an academic tutor and the owner of Simplifi EDU, a Santa Monica, California based online tutoring business offering learning resources and online tutors for academic subjects K-College, SAT & ACT prep, and college admissions applications. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. Jake holds a BS in International Business and Marketing from Pepperdine University.An extraneous solution refers to a result that may appear valid when substituting a certain value for X in an equation, but it often leads to a situation where the expression becomes indeterminate, such as division by zero. When working with the original (parent) function, extraneous solutions may not be immediately apparent, as simplification steps can eliminate them. However, upon revisiting the original function, plugging in an extraneous solution may render the function undefined or result in a zero-over-zero scenario. In essence, extraneous solutions are deemed irrelevant as they don't contribute valid answers to the problem, given that zero over zero or undefined values are not considered part of the solution set.
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QuestionHow do I solve a one-step equation that looks like this: 8.7x = 45?I_l1ke_gam3sCommunity AnswerDivide both sides by 8.7 so that x is isolated. You get x = 5.17.
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QuestionHow can I make a problem into an equation?Community AnswerLet some variable (such as x) represent the quantity you're looking for. Then express in mathematical terms the conditions set forth in the problem. For example, if you're told, "three times a number plus 30 equals 45. What's the number?" you'd let x be the unknown number. Then "3x" is "three times the number," and "3x + 30" is "three times the number plus 30." Finally, "three times a number plus 30 equals 45" is expressed as "3x + 30 = 45." When you solve that equation you find that x = 5.
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References
- ↑ https://www.mathsisfun.com/definitions/equation.html
- ↑ http://www.purplemath.com/modules/solvelin.htm
- ↑ https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-one-step-add-sub-equations/v/solving-one-step-equations
- ↑ https://www.mathsisfun.com/algebra/equations-solving.html
- ↑ http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_OneVariableOneStep.xml
- ↑ https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-solving-equations/v/why-we-do-the-same-thing-to-both-sides-simple-equations
- ↑ https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-one-step-mult-div-equations/a/one-step-equation-review
- ↑ https://www.chilimath.com/lessons/introductory-algebra/solving-one-step-equations/
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