SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS By Noel Platt
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS RULE 1:
Whatever you do to one side of an ‘=‘ you do to the other. For example:
2 = 2
2+1 = 2+1 (if you add 1 to both sides of = )
(2+1)2 =(2+1)2 (if you Square both sides of =)
Similarly:
X = 2
x+1 = 2+1 (if you add 1 to both sides of =)
(x+1)2 =(2+1)2 (if you Square both sides of =)
Etc.
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS RULE 2:
The law of opposites:
Operation Opposite
+5 -5
-14 +14
X 22.5 /22.5
/16.03 x16.03
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS RULE 3:
The order in which you apply the rule of opposites is the reverse of BODMAS.
SAMDOB.
BODMAS is tying up your shoe laces and SAMDOB is untying them. This is necessary when solving equations because we are doing the opposite of evaluating a formula.
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS RULE 4:
One side of the equal sign can be replaced with a SIMPLIFIED version that MEANS THE SAME THING in a Re Written form.
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS Solve the following equation:
X + 4 = 6 SOLUTION
Opposite of + 4 is -4 (rule 2)
-4 from both sides of equal sign (rule 1)
X + 4 = 6 (State Eqtn)
X + 4 – 4 = 6 – 4
X = 2
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS Solve the following equation:
X -3 = 12 SOLUTION
Opposite of -3 is +3 (rule 2)
+3 to both sides of equal sign (rule 1)
X -3 = 12 (State eqtn)
X -3+3 = 12 +3
X = 15
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS Solve the following equation:
X /3 = 12 SOLUTION
Opposite of /3 is x3 (rule 2)
x3 to both sides of equal sign (rule 1)
X /3 = 12 (State eqtn)
X /3x3 = 12 x3
X = 36
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS Solve the following equation:
4y = 20 SOLUTION
Opposite of x4 is /4 (rule 2)
Divide both sides of equal sign by 4 (rule 1)
4y = 20 (state eqtn)
4y/4 = 20/4
Y = 5
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS Solve the following equation:
3p +5 = 17
SOLUTION
By rule 3 (SAMDOB) reverse Addition before reversing multiplication
Subtract 5 from both sides first.
3p +5 = 17 (State eqtn)
3p +5-5 = 17-5
3p = 12
Divide both sides by 3
3p/3 = 12/3
P = 4
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS Solve the following equation:
2m -11 = 9
SOLUTION
By rule 3 (SAMDOB) reverse subtraction before reversing multiplication
Add 11 to both sides first.
2m-11 = 9 (state equtn)
2m-11+11 = 9+11
2m = 20
Divide both sides by 2
2m/2 = 20/2
m = 10
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS Solve the following equation:
4(x-1) = 36
SOLUTION
Re-write L. H S of ‘=‘ without brackets.
4(x-1) = 36
4x – 4 = 36
Add 4 to both sides
4x – 4+4 = 36+4
4x = 40
Divide both sides by 4
4x /4 = 40/4
X = 10
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS Solve the following equation:
22x + 5(1-3x) = 19 SOLUTION
Re write L.H.S of ‘=‘ without brackets & simplify:
22x + 5(1-3x) = 19
22x +5 – 15x = 19
7x + 5 = 19
Subtract 5 from both sides
7x + 5-5 = 19-5
7x = 14
Divide both sides by 7
7x/7 = 14/7
X = 2
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS Solve the following equation:
2(x-1) +4(2x+4) = 20
SOLUTION:
Re write L.H.S of ‘=‘ without brackets & simplify:
2(x-1) +4(2x+4) = 20
2x -2 +8x+16 =20
10x +14 =20
Subtract 14 from both sides
10x +14-14 =20-14
10x = 6
Divide both sides by 10
10x/10 = 6/10
X = 0.6
SOLVING LINEAR EQUATIONS : SOLVING LINEAR EQUATIONS Solve the following equation:
2x +1 = 3x -5
SOLUTION:
Bring all x terms to R.H.S (-2x from both sides)
2x +1 = 3x -5
2x +1-2x = 3x -5-2x
1 = x -5
Add 5 to both sides.
1+5 = x -5+5
6 = x