1
Use the Equation 4 + 21x = 17 to identify its parts.
a. what are the constants?
b. what are the variables?
c. what are the terms?
a. 4, 17, 21
b. x
c. 4, 21x, 17
Write an equation for each sentence (you do not have to solve).
Twice a number is equal to -54.
2n = -54
Write an equation for each sentence (you do not have to solve).
Nineteen less than a number is 3
n - 19 = 3
Choose the best equation to represent the situation.
The new oil rigs belonging to Pa's Gas can drill downward 930 ft farther than the old ones, to a depth of -7440 ft. To what depth could they drill before?
a. d + 930 = -7440 b. d - 930 = -7440
c. -930d = 7440 d. d/930 = 7440
b. d - 930 = -7440
Determine whether the given value is a solution for the equation.
-12 = 7y - 9 when y = -3
-12 = 7(-3) - 9
-12 = -30
NO
t + 2 = 4
t = 2
Is the inequality symbol reversed within the solution of
20 >= -6x?
Yes, the inequality symbol is reversed within the solution because the variable x has a negative coefficient.
-7c = -147
c = 21
u - 4 = 7
u = 11
12 = (-3/4)t
t = -16
w/4 = 3
w = 12
7x + 3x = 30
x = 3
4 + g/7 = -3
g = -49
2/3y - 8 = 10
y = 27
a - 13 < 7
a < 20
Translate each sentence into an algebraic equation, then solve.
Five less than the product of 8 and b is -1.
8b - 5 = -1; b = 1/2
Determine whether the given value is a solution for each inequality.
47 > - 2 - 9/2j; j = -20
no ; 47 > 88
Explain the process needed to solve the equation in two steps.
4(y + 8) = 16
Divide by 4; subtract 8.
2(x + 4) = 36
x = 14
Translate each sentence into an algebraic equation, then solve.
Four more than the quotient of z and 7 is 19.
z/7 + 4 = 19; z = 105
2/13(12p + 25) = 26
p = 12
Write an inequality for each sentence.
The difference of 11 and r is at most 23.
11 - r <= 23
Write an inequality for each sentence.
The quotient of q and -5 is greater than 16.
q/-5 > 16
Write an inequality for each sentence.
Which inequality below has a given value that is not a solution.
A. 8 - 3p > 9; p = 7
B. e - 4 < 3; e = 3
C. n/-5 <= 7; n = -35
D. none of these
A. 8 - 3p > 9; p = 7
x/15 >= 15
x >= 225
Solve the inequality.
5/6(18j -12) ≠ 20
j ≠ 2
Solve each inequality, and then graph the solution set on a number line.
-2c <= 8
c >= -4
Determine whether the given value is a solution for each inequality.
4c - 3 <= 17; c = 0
yes; -3 <= 17
9(a - 2) = -54
a = -4
-7/2v >= -14
v <= 4
s - (-6 1/7) = 4 9/14
s = -1 1/2
Write an inequality for each sentence.
Two less than the quotient of a and 2 is greater than 15.
a/2 - 2 > 15
Write an inequality for each sentence.
The sum of 29 and -1/3 of w is at least 43.
29 + (-1/3w) >= 43
Write and solve an equation to answer the question.
Sarah spent 3 hours preparing all her watercolors and 2 hours painting each watercolor. How many watercolors did she paint if her work consumed a total of 13 hours?
3 + 2w = 13; w = 5
Solve each inequality, and then graph the solution set on a number line.
r - (-8) ≠ -9
r ≠ -17
Tamir says that x = -3 is in the solution set for
4x - (-13) ≠ 1
Is he correct? Explain.
Tamir is incorrect.
Solving the inequality by subtracting 13 from both sides and dividing both sides by 4 would result in
x ≠ -3
Write and solve an equation to answer each question.
For 5 straight days, the soccer players had to run 6 more laps per day than the tennis players. If the soccer players ran a total of 45 laps, how many laps did the tennis players run each day?
5(n + 6) = 45
n = 3 laps
Write and solve an equation to answer each question.
In Mohe City, China, the high temperature today is -27°F, which is 11°F less than yesterday's high temperature. What was the high temperature yesterday?
t - 11 = -27
t = -16°F
Write and solve an equation to answer each question.
Jayden has begun reading 3 chapters of the Old Testament per day. He has now read 57 chapters in the Old Testament. How many days has he been reading?
3d = 57
d = 19 days
y - 12 4/9 > 8 5/9
y > 21