How to Solve Two Step Algebraic Equations

byMR Munna -
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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.

[Edit]Steps

[Edit]Solving Equations with One Variable

  1. Write 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]
    Solve Two Step Algebraic Equations Step 1 Version 4.jpg
  2. Decide whether to use addition or subtraction to isolate the variable term.[2] 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]
    Solve Two Step Algebraic Equations Step 2 Version 4.jpg
  3. Add 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.[4]
    Solve Two Step Algebraic Equations Step 3 Version 4.jpg
    • -4x + 7 = 15 =
    • -4x = 8
  4. Eliminate 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.
    Solve Two Step Algebraic Equations Step 4 Version 4.jpg
  5. Solve 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.
    Solve Two Step Algebraic Equations Step 5 Version 5.jpg

[Edit]Solving Equations with One Variable on Each Side

  1. Write 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.[5]
    Solve Two Step Algebraic Equations Step 6 Version 3.jpg
  2. Move 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.[6]
    Solve Two Step Algebraic Equations Step 7 Version 3.jpg
    • 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
  3. Move 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.[7] On the left side, -2x - 4x = -6x, and on the right side, (4x -12) -4x = -12, so the new equation should read -6x = -12.
    Solve Two Step Algebraic Equations Step 8 Version 3.jpg
    • -2x - 4x = (4x - 12) - 4x = -6x = -12
  4. Solve 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.
    Solve Two Step Algebraic Equations Step 9 Version 3.jpg
    • -6x ÷ -6 = -12 ÷ -6
    • x = 2

[Edit]Other Ways to Solve Two-Step Equations

  1. Solve two-step 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:[8]
    Solve Two Step Algebraic Equations Step 10 Version 3.jpg
    • 11 = 3 - 7x =
    • 11 - 3 = 3 - 3 - 7x =
    • 8 = - 7x =
    • 8/-7 = -7/7x
    • -8/7 = x or -1.14 = x
  2. Solve 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:
    Solve Two Step Algebraic Equations Step 11 Version 3.jpg
    • x/5 + 7 = -3 =
    • (x/5 + 7) - 7 = -3 - 7 =
    • x/5 = -10
    • x/5 * 5 = -10 * 5
    • x = -50

[Edit]Video

[Edit]Tips

  • Read the question carefully.
  • 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.[9]
  • If there is no number in front of the x, assume it is a 1x.
  • There may not be an explicit constant on each side. If there is no number following an x, assume it is x + 0.

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[Edit]Quick Summary

[Edit]References

  1. ↑ https://www.registerednursing.org/teas/solving-equations-one-variable/
  2. ↑ https://www.montereyinstitute.org/courses/DevelopmentalMath/TEXTGROUP-9-14_RESOURCE/U10_L1_T1_text_container.html
  3. ↑ http://sites.austincc.edu/tsiprep/math-review/equations/a-general-rule-for-solving-equations/
  4. ↑ https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-variables-on-both-sides/v/equations-3
  5. ↑ http://www.algebra-class.com/algebra-equations.html
  6. ↑ https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-two-steps-equations-intro/v/solving-equations-1
  7. ↑ https://www.montereyinstitute.org/courses/DevelopmentalMath/TEXTGROUP-9-14_RESOURCE/U10_L1_T2_text_container.html
  8. ↑ https://www.chilimath.com/lessons/intermediate-algebra/solving-two-step-equations/
  9. ↑ http://www.math.com/school/subject1/lessons/S1U1L12DP.html


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