solving equations
a. x − 3 = −5
x = −2
x + 8 < −3
4 < −3
Evaluate 4x − 5 when x = 3.
= 7
Substitute 2 for x
x + y = 7
2 + 5 = 7
7 = 7
Write an equation for the nth term of the arithmetic sequence 5, 15, 25, 35,
The first term is 5, and the common difference is 10.
an = a1 + (n − 1)d
an = 5 + (n − 1)(10)
an = 10n − 5
y+2.8=0.9
y = −1.9.
−4.5x > −21
18 > −21
Evaluate −2x + 9 when x = −8.5.
=26
5 for y
2x − 3y = −11
2(2) − 3(5) =
? −11
−11 = −11
a. y = −2(5)x; x = 3
-250
c. 1.3z = 5.2
z = 4
−3 ≤ 1
−8 ≤ −4
h + 6 = −7
h=-13
Substitute −2 for x
y = −2x − 4
0 =
? −2(−2) − 4
0 = 0
The value t = 4 represents the fi fth year because t = 0 represents the fi rst year.
y = 150,000(1.08)t
≈ 204,073
2.5x − 13 = 2
The solution is x = 6
y + 8 ≤ 5
The solution is y ≤ −3.
Evaluate f(x) = −4x + 7 when x = 2
-1
6x − 5y = −19 Equation 2
6x − 5(−2x − 9) = −19 Substitute −2x − 9 for y.
6x + 10x + 45 = −19 Distributive Property
16x + 45 = −19 Combine like terms.
16x = −64
x = −4
The initial value is $21,500, and the rate of decay is 12%, or 0.12.
y = a(1 − r)t
21,500(0.88)t
−12 = 9x − 6x + 15
The solution is x = −9.
−6 < 8
−12 < 16
Use intercepts to graph the equation 3x + 4y = 12.
SOLUTION
Step 1 Find the intercepts.
To find the x-intercept, substitute 0 for y and solve for x.
3x + 4y = 12
x = 4
3 Substitute −4 for x in Equation 1 and solve for y.
y = −2x − 9
= −2(−4) − 9
= 8 − 9
= −1
Write an equation for the nth term of the geometric sequence
2, 12, 72, 432, . . .. Then fi nd a10.
SOLUTION
The fi rst term is 2, and the common ratio is 6.
= 20,155,392