An equation is a mathematical statement that two expressions have the same value, which are separated by an equal sign, “=”.
To solve multi step equations, we should know about inverse operations.
Note :
If it is required, we may use the distributive property.
Solve each of the following equation.
Problem 1 :
-3m - 5 = 5m - 13
Solution :
Subtract 5m from both sides.
-3m - 5 - 5m = 5m -13 - 5m
-8m - 5 = -13
Add 5 to both sides.
-8m - 5 + 5 = -13 + 5
-8m = -8
Divide both sides by -8.
m = 1
So, the solution of m is 1.
Problem 2 :
6(y + 7) = 2(y - 3)
Solution :
6(y + 7) = 2(y - 3)
By distributing 6 and 2, we get
6y + 42 = 2y - 6
Subtract 2y from both sides.
6y + 42 - 2y = 2y - 6 - 2y
4y + 42 = -6
Subtract 42 from both sides.
4y + 42 - 42 = -6 - 42
4y = -48
Divide both sides by 4.
4y/4 = -48/4
y = -12
So, the solution of y is -12.
Problem 3 :
10q + 3q + 5 = 2(q - 3)
Solution :
10q + 3q + 5 = 2(q - 3)
10q + 3q + 5 = 2q - 6
13q + 5 = 2q - 6
Subtract 2q from both sides.
13q + 5 - 2q = 2q - 6 - 2q
11q + 5 = -6
Subtract 5 from both sides.
11q + 5 - 5 = -6 - 5
11q = -11
Divide both sides by 11.
11q/11 = -11/11
q = -1
So, the solution of q is -1.
Problem 4 :
(1/3)(x + 6) = (2/3)(x - 9)
Solution :
(1/3)(x + 6) = (2/3)(x - 9)
By distributing 1/3 and 2/3, we get
(x + 6)/3 = (2x - 18)/3
Multiply by 3 on both sides,
x + 6 = 2x - 18
Subtract 6 from both sides.
x = 2x - 18 - 6
x = 2x - 24
Subtract 2x from both sides.
x - 2x = 2x - 24 - 2x
-x = -24
x = 24
So, the solution of x is 24.
Problem 5 :
8k+12=2(k-3)
Solution :
8k + 12 = 2(k - 3)
8k + 12 = 2k - 6
Subtract 2k from both sides.
8k + 12 - 2k = 2k - 6 - 2k
6k + 12 = -6
Add 6 from both sides.
6k + 12 + 6 = -6 + 6
6k + 18 = 0
6k = -18
Divide both sides by 6.
6k/6 = (-18)/6
k = -3
So, the solution of k is -3.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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