Solving two-step equations

When solving two-step equations, they will have the following form: ax + b = c  or ax − b = c

When solving equations of the form ax + b = c, you can subtract b from both sides of the equation and then divide both sides by a.

ax + b = c

ax + b - b = c - b

ax + 0 = c - b

ax = c - b

ax/a = (c - b)/a

x = (c - b)/a

When solving equations of the form ax − b = c, you can add b to both sides of the equation and then divide both sides by a.

ax - b = c

ax - b + b = c + b

ax + 0 = c + b

ax = c + b

ax/a = (c + b)/a

x = (c + b)/a

Now, let us see how we can solve two-step equations using numbers instead of letters.

Example #1:

solving-two-step-equations

Example #2: You can solve the problem above by dividing both sides by a first before adding or subtracting something from both sides.

solving-two-step-equations

Example #3:

solving-two-step-equations

Solving two-step equations involving fractions.

Example #4:

solving-two-step-equations-involving-fractions

Note that there is nothing special about subtracting b or adding b to both sides and then then divide by a!

You can instead start by dividing both sides by a and then subtract or add something to both sides. You will end up with the same answer as you can see from example #1 and example #2.

In practice, mathematicians prefer to add or subtract something from both sides and then divide by a because calculations are usually easier.

Let us solve example #4 by dividing both sides by 2/5 first. 

(2/5)x + 4 = 14

Divide both sides by 2/5

[(2/5) ÷ (2/5)]x + 4 ÷ 2/5 = 14 ÷ 2/5

[1]x + 4/1 ÷ 2/5 = 14/1 ÷ 2/5

x + 4/1 × 5/2 = 14/1 × 5/2

x + 20/2 = 70/2

x + 10 = 35

Subtract 10 from both sides

x + 10 - 10 = 35 - 10

x + 0 = 25

x = 25

The super fast way to solve two-step equations.

When taking a test, there is no need to follow all the steps above if all you need to do is to choose the right answer from a list of multiple choices.

To solve ax + b = c, just use x = (c - b)/a

You can solve example #3 or 6x + 2 = 20 very fast.

x = (20 - 2)/6 = 18/6 = 3

Similarly, you can solve example #1 or 2x - 2 = 8 very fast.

x = (c + b)/a = (8 + 2)/2 = 10/2 = 5

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