When fixing two-step equations, these equations could have the next linear type: ax + b = c or ax − b = c, the place a is named coefficient and b and c are referred to as constants.
In fact, solely two steps are wanted as proven beneath:
Step 1
Isolate ax
Step 2
Isolate x
Bear in mind additionally the Golden Rule of Algebra. No matter you do to 1 facet of an equation, you will need to additionally do the identical to the opposite facet of the equation with a view to hold the equation balanced.
Fixing two-step equations of the shape ax – b = c
Instance #1
Remedy 2x – 2 = 6
Step 1:
Isolate 2x by including 2 to each side of 2x – 2 = 6
2x – 2 + 2 = 6 + 2
2x = 8
Step 2:
Divide each side of 2x = 8 by 2 to isolate x
2x / 2 = 8 / 2
x = 4
You may examine to see if x = 4 is certainly an answer by changing 4 within the authentic equation.
2(4) – 2 = 8 – 2 = 6 ✓
Typically talking, when fixing equations of the shape ax − b = c, you may add b to each side of the equation to isolate ax (step 1) after which divide each side by a to isolate x (step 2).
ax – b = c
Step 1:
ax – b + b = c + b
ax + 0 = c + b
ax = c + b
Step 2:
ax/a = (c + b)/a
x = (c + b)/a
Fixing two-step equations of the shape ax + b = c
Instance #2
Remedy 6x + 2 = 20
Step 1:
Isolate 6x by subtracting 2 from each side of 6x + 2 = 20
6x + 2 – 2 = 20 – 2
6x = 18
Step 2:
Divide each side of 6x = 18 by 6 to isolate x
6x / 6 = 18 / 6
x = 3
Basically, when fixing equations of the shape ax + b = c, you may subtract b from each side of the equation to isolate ax (step 1) after which divide each side by a to isolate x (step 2).
ax + b = c
Step 1:
ax + b – b = c – b
ax + 0 = c – b
ax = c – b
Step 2:
ax/a = (c – b)/a
x = (c – b)/a
There’s nothing particular about subtracting b or including b to each side after which divide by a! In observe, mathematicians desire so as to add or subtract one thing from each side after which divide by a as a result of calculations are often simpler.
Discover although that there’s one other solution to clear up instance #1 above with simply two steps as properly.
1. Step one is to divide each side of the equation by a
2. The second step is to both add one thing to each side of the brand new equation or subtract one thing from each side of the brand new equation.
Remedy 2x – 2 = 6 by following the 2 steps outlined instantly above
Step 1:
Divide each side of 2x – 2 = 6 by 2
(2x – 2) / 2 = 6 / 2
x – 1 = 3
Step 2:
Add 1 to each side of x – 1 = 3
x – 1 + 1 = 3 + 1
x = 4
Fixing two-step equations involving fractions
Instance #3
Remedy (2/5)x + 4 = 14
Step 1:
Isolate (2/5)x by subtracting 4 from each side of (2/5)x + 4 = 14
(2/5)x + 4 – 4 = 14 – 4
(2/5)x = 10
Step 2:
Multiply each side of (2/5)x = 10 by the reciprocal of two/5 or 5/2.
(5/2)(2/5)x = 10(5/2)
(10/10)x = 50/2
x = 25
Once more, we will additionally clear up instance #3 by dividing each side by 2/5 first.
(2/5)x + 4 = 14
Divide each side 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 each side
x + 10 – 10 = 35 – 10
x + 0 = 25
x = 25
Fixing two-step equations involving decimals
The steps to comply with are the identical when fixing two-step equations involving decimals.
Instance #4
Remedy 3.1x + 1.2 = 7.4
Subtract 1.2 from each side of 3.1x + 1.2 = 7.4 to isolate 3.1x
3.1x + 1.2 – 1.2 = 7.4 – 1.2
3.1x = 6.2
Divide each side of three.1x = 6.2 by 3.1 to isolate x
(3.1x)/3.1 = 6.2/3.1
x = 2
The tremendous quick solution to clear up two-step equations.
When taking a check, there isn’t a have to comply with all of the steps above if all you could do is to decide on the fitting reply from an inventory of a number of selections.
To resolve ax + b = c, simply use x = (c – b)/a
You may clear up instance #2 or 6x + 2 = 20 very quick.
x = (20 – 2)/6 = 18/6 = 3
Equally, you may clear up instance #1 or 2x – 2 = 6 very quick.
x = (c + b)/a = (6 + 2)/2 = 8/2 = 4
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