solve the modulus equations below. (a) |2x+3|=6. (b) |x-2|=x+4. (c) |2x-7|=|x+3|
1 answer:
Answer:
(a) x=1.5 or x=-4.5
(b) x=-1
(c) x=10 or
Step-by-step explanation:
(a) |2x+3|=6
⇒ 2x+3=6 or 2x+3=-6
⇒ 2x=3 or 2x=-9
⇒ x=1.5 or x=-4.5
(b) |x-2|=x+4
⇒ x-2=x+4 or x-2=-(x+4)
x-2=x+4
-2≠4 x∈Ф
or x-2=-(x+4)
x-2=-x-4
2x=-2
x=-1
(c) |2x-7|=|x+3|
⇒ 2x-7=x+3 or 2x-7=-(x+3)
2x-7=x+3
x=10
or 2x-7=-(x+3)
2x-7=-x-3
3x=4
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Answer:
7x - 3y = 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 3x + 7y = 15 into this form
Subtract 3x from both sides
7y = - 3x + 15 ( divide all terms by 7 )
y = - x +
← in slope- intercept form
with slope m = -
Given a line with slope m the the slope of a line perpendicular to it is
= -
= -
=
, thus
y = x + c ← is the partial equation of the line
To find c substitute (4, 9) into the partial equation
9 = + c ⇒ c -
y = x -
← in slope- intercept form
Multiply through by 3
3y = 7x - 1 ( subtract 3y from both sides )
0 = 7x - 3y - 1 ( add 1 to both sides )
1 = 7x - 3y, that is
7x - 3y = 1 ← in standard form