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.
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
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
Linear equations calculatorOct 14, 21 05:41 AM
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