Question; Solve each equation: PRELIMINARIES (A) 2x + 8 = x − 4 (B) 3r + 2 − 5(r + 1) = 6r + 4 (C) x 2sequer + 5x + 6 = 0
Answers
Answer:
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Step-by-step explanation:
a) 2x+8=x-4
2x+x=8-4
3x=4
x=4/3
b) 3r+2-5(r+1)=6r+4
Reorder the terms:
3r + 2 + -5(1 + r) = 6r + 4
3r + 2 + (1 * -5 + r * -5) = 6r + 4
3r + 2 + (-5 + -5r) = 6r + 4
Reorder the terms:
2 + -5 + 3r + -5r = 6r + 4
Combine like terms: 2 + -5 = -3
-3 + 3r + -5r = 6r + 4
Combine like terms: 3r + -5r = -2r
-3 + -2r = 6r + 4
Reorder the terms:
-3 + -2r = 4 + 6r
Solving
-3 + -2r = 4 + 6r
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Add '-6r' to each side of the equation.
-3 + -2r + -6r = 4 + 6r + -6r
Combine like terms: -2r + -6r = -8r
-3 + -8r = 4 + 6r + -6r
Combine like terms: 6r + -6r = 0
-3 + -8r = 4 + 0
-3 + -8r = 4
Add '3' to each side of the equation.
-3 + 3 + -8r = 4 + 3
Combine like terms: -3 + 3 = 0
0 + -8r = 4 + 3
-8r = 4 + 3
Combine like terms: 4 + 3 = 7
-8r = 7
Divide each side by '-8'.
r = -0.875
Simplifying
r = -0.875
c)
The solutions are
x
=
2
,
x
=
3
Explanation:
x
2
−
5
x
+
6
=
0
Here we can first factorise the expression and then find the solution:
Factorising by splitting middle term
x
2
−
2
x
−
3
x
+
6
=
0
x
(
x
−
2
)
−
3
(
x
−
2
)
=
0
(
x
−
2
)
(
x
−
3 )
=
0
Equating the two factors with zero to obtain solutions:
x
−
2
=
0
,
x
=
2
x
−
3
=
0
,
x
=
3