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Two step algebraic equations are relatively quick and easy  after all, they should only take two steps. To solve a two step algebraic equation, all you have to do is isolate the variable by using either addition, subtraction, multiplication, or division. If you want to know how to solve two step algebraic equations in a variety of ways, just follow these steps.
Steps
Method 1
Method 1 of 3:Solving Equations with One Variable
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1Write the problem. The first step to solving a two step algebraic equation is just to write the problem so you can start to visualize the solution. Let's say we're working with the following problem: 4x + 7 = 15.^{[1] X Research source }

2Decide whether to use addition or subtraction to isolate the variable term.^{[2] X Research source } The next step is to find a way to keep "4x" on one side and to keep the constants (whole numbers) on the other side. To do this, you'll have to do the "Additive Inverse," finding the opposite of +7, which is 7. Subtract 7 from both sides of the equation so that the "+7" on the same side as the variable term is canceled out. Just write "7" below the 7 on one side and below the 15 on the other so the equation remains balanced.^{[3] X Research source }
Remember the Golden Rule of Algebra. Whatever you do to one side of an equation must be done to the other side to maintain the balance.^{[4] X Research source } That is why 7 is subtracted from the 15 as well. We only need to subtract 7 once per side, which is why the 7 is not subtracted from the 4x as well.
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3Add or subtract the constant on both sides of the equation. This will complete the process of isolating the variable term. Subtracting 7 from +7 on the left side of the equation will leave no constant term (or 0) on the left side of the equation. Subtracting 7 from +15, on the right side of the equation, will leave you with 8. Therefore, the new equation is 4x = 8.^{[5] X Research source }
 4x + 7 = 15 =
 4x = 8

4Eliminate the coefficient of the variable through division or multiplication. The coefficient is the number attached to the variable. In this example, the coefficient is 4. To remove the 4 in 4x, you'll have to divide both sides of the equation by 4. Right now, the x is being multiplied by the 4, so the opposite of this operation is division and you'll have to do it on both sides.
Again, whatever you do to the equation must be done to both sides. That is why you see ÷ 4 twice.

5Solve for the variable. To do this, divide the left side of the equation, 4x, by 4, to get x. Divide the right side of the equation, 8, by 4, to get 2. Therefore, x = 2. You've taken two steps  subtraction and division  to solve this equation.Advertisement
Method 2
Method 2 of 3:Solving Equations with One Variable on Each Side
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1Write the problem. The problem you will be working with is the following: 2x  3 = 4x  15. Before you proceed, make sure that both of the variables are the same. In this case, "2x" and "4x" both have the same variable, "x," so you can move forward.^{[6] X Research source }

2Move the constants to the right side of the equation. To do this, you'll need to use addition or subtraction to eliminate the constant from the left side of the equation. The constant is 3, so you'll have to take its opposite, +3, and add this constant to both sides of the equation.^{[7] X Research source }
 Adding +3 to the left side of the equation, 2x 3, will give you (2x 3) + 3, or 2x on the left side.
 Adding +3 to the right side of the equation, 4x 15, will give you (4x  15) +3, or 4x 12.
 Therefore, (2x  3) +3 = (4x  15) +3 = 2x = 4x  12
 The new equation should read 2x = 4x 12

3Move the variables to the left side of the equation. To do this, you'll simply have to take "the opposite" of "4x", which is "4x," and subtract 4x from both sides of the equation.^{[8] X Research source } On the left side, 2x  4x = 6x, and on the right side, (4x 12) 4x = 12, so the new equation should read 6x = 12.
 2x  4x = (4x  12)  4x = 6x = 12

4Solve for the variable. Now that you've simplified the equation to 6x = 12, all you have to do is to divide both sides of the equation by 6 to isolate the variable x, which is currently being multiplied by 6. On the left side of the equation, 6x ÷ 6 = x, and on the right side of the equation, 12 ÷ 6 = 2. Therefore, x = 2.
 6x ÷ 6 = 12 ÷ 6
 x = 2
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Method 3
Method 3 of 3:Other Ways to Solve TwoStep Equations
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1Solve twostep equations while keeping the variable on the right side. You can solve a two step equation while keeping the variable on the right side. As long as you isolate it, you'll still get the same answer. Let's take the problem, 11 = 3  7x. To solve it, your first step will be to combine the constants by subtracting 3 from both sides of the equation. Then, you'll have to divide both sides of the equation by 7 to solve for x. Here's how you do it:^{[9] X Research source }
 11 = 3  7x =
 11  3 = 3  3  7x =
 8 =  7x =
 8/7 = 7/7x
 8/7 = x or 1.14 = x

2Solve a two step equation by multiplying at the end instead of dividing. The principle for solving this type of equation is the same: use arithmetic to combine the constants, isolate the variable term, and then isolate the variable without the term. Let's say you're working with the equation x/5 + 7 = 3. The first thing you should do is subtract 7, the inverse of 3, from both sides, and then multiply both sides by 5 to solve for x. Here's how you do it:
 x/5 + 7 = 3 =
 (x/5 + 7)  7 = 3  7 =
 x/5 = 10
 x/5 * 5 = 10 * 5
 x = 50
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Community Q&A

QuestionHow do I solve x/5  8 = 7?Community AnswerThe goal is to get x on one side of the equation. So add 8 to both sides of the equation; x/5  8 + 8 = 7 + 8; x/5 = 15. Next, multiply both sides of the equation by 5. 5 (x/5) = 15 (5). x = 75.

QuestionHow would I solve 5x  6 = 3(x1)?DonaganTop Answerer5x  6 = 3x  3. Subtract 3x from both sides: 2x  6 = 3. Add 6 to both sides: 2x = 3, so x = 3/2.

QuestionHow do I solve (3x  2y) squared?DonaganTop Answerer9x² 12xy+4y². It's figured this way: (3x)(3x) = 9x². (3x)(2y) = 6xy, and (2y)(3x) = 6xy; (6xy) + (6xy) = 12xy. (2y)(2y) = +4y².

QuestionHow do I solve 1/4x + 7 = 9?DonaganTop AnswererMultiply both sides by 4 to get rid of the fraction: x + 28 = 36. Subtract 28 from both sides: x = 64.

QuestionHow would I solve for f in the equation C = 5/9 (f  32)?DonaganTop Answererf = [(9/5)C] + 32.

QuestionHow do I calculate x + y = 10  y = 2?DonaganTop AnswererStart with 10  y = 2. Adding y to both sides and subtracting 2 from both sides, we see that 8 = y. Then we insert that value of y into x + y = 2 and find that x = 6. Check by inserting those values of x and y into the full equation: 6 + 8 = 10  8 = 2.

QuestionI don't know how to solve verbal problems like these. What should I do?DonaganTop AnswererLet a variable (such as x) stand for the number you're looking for. Set up an equation in x that expresses the conditions described in the problem, and solve the equation for x. It takes some practice to become good at setting up such an equation, because every problem is slightly different. Ask for help from someone who knows how to do it, and then keep practicing.

QuestionWhat if there is no operation in the answer?DonaganTop AnswererThat's fine. The answer does not have to have any operation.

QuestionHow do I solve 7x + 9 = 23?DonaganTop AnswererSubtract 9 from both sides of the equation, then divide both sides by 7.

QuestionHow do I solve 4x + 7  6 = 5  4x + 4?DonaganTop AnswererFirst simplify both sides of the equation: 4x + 1 = 9  4x. Then add 4x to both sides and subtract 1 from both sides: 8x = 8. Then divide both sides by 8.
Video
Tips
 Read the question carefully.Thanks!
 When multiplying or dividing two numbers with different signs, (i.e., one positive & the other negative) the result is always negative. If both signs matched, then the solution would be a positive number.^{[10] X Research source }Thanks!
 If there is no number in front of the x, assume it is a 1x.Thanks!
 There may not be an explicit constant on each side. If there is no number following an x, assume it is x + 0.Thanks!
References
 ↑ https://www.registerednursing.org/teas/solvingequationsonevariable/
 ↑ https://www.montereyinstitute.org/courses/DevelopmentalMath/TEXTGROUP914_RESOURCE/U10_L1_T1_text_container.html
 ↑ http://sites.austincc.edu/tsiprep/mathreview/equations/ageneralruleforsolvingequations/
 ↑ http://hyperphysics.phyastr.gsu.edu/hbase/alg2.html#ag
 ↑ https://www.khanacademy.org/math/algebra/onevariablelinearequations/alg1variablesonbothsides/v/equations3
 ↑ http://www.algebraclass.com/algebraequations.html
 ↑ https://www.khanacademy.org/math/algebra/onevariablelinearequations/alg1twostepsequationsintro/v/solvingequations1
 ↑ https://www.montereyinstitute.org/courses/DevelopmentalMath/TEXTGROUP914_RESOURCE/U10_L1_T2_text_container.html
 ↑ https://www.chilimath.com/lessons/intermediatealgebra/solvingtwostepequations/
About This Article
To solve two step algebraic equations with a variable on 1 side, start by using addition or subtraction to isolate the variable term. For example, if the equation is 4x + 7 = 15, isolate 4x by subtracting 7 from both sides, so that the equation becomes 4x = 8. Next, divide 4x by the number in front of the variable, so that you are left with only x. Finally, divide the other side by the same number to get x = 2. To learn more, including how to solve algebraic equations with a variable on both sides, scroll down.