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When fixing two-step equations, these equations can have the next linear type: ax + b = c or ax − b = c, the place a known as coefficient and b and c are known as constants.
After all, solely two steps are wanted as proven under:
Step 1
Isolate ax
Step 2
Isolate x
Bear in mind additionally the Golden Rule of Algebra. No matter you do to at least one aspect of an equation, you have to additionally do the identical to the opposite aspect of the equation to be able to maintain the equation balanced.
Fixing two-step equations of the shape ax – b = c
Instance #1
Clear up 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 unique equation.
2(4) – 2 = 8 – 2 = 6 ✓
Usually talking, when fixing equations of the shape ax − b = c, you possibly can 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
Clear up 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
Typically, when fixing equations of the shape ax + b = c, you possibly can 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 want 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 resolve instance #1 above with simply two steps as effectively.
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.
Clear up 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
Clear up (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 resolve 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
Clear up 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 resolve two-step equations.
When taking a take a look at, there is no such thing as a must comply with all of the steps above if all it’s essential to do is to decide on the suitable reply from an inventory of a number of decisions.
To resolve ax + b = c, simply use x = (c – b)/a
You may resolve instance #2 or 6x + 2 = 20 very quick.
x = (20 – 2)/6 = 18/6 = 3
Equally, you possibly can resolve instance #1 or 2x – 2 = 6 very quick.
x = (c + b)/a = (6 + 2)/2 = 8/2 = 4
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