Download Chapter 4: First degree equations and

Chapter 4: First degree equations and inequalities in one variable
Which of the following is not an equation?
1. 5(x2 - 3)
2. x2 - 6x = 9
3.
4.
Given the statement: 5 less than 3 times a number is greater than 4 times that same number.
Which is another way to write the given statement?
1.
2.
3.
4.
3x - 5 > 4x
3x - 5 < 4x
5 - 3x ≥ 4x
3x - 5 ≤ 4x
What is another way to express the following statement?
"Eight times a number increased by 10 is no more than 20."
1.
2.
3.
4.
8x - 10 > 20
8x + 10 ≤ 20
10 + 8x > 20
8x + 10 ≥ 20
The square of a number, increased by 2, is no less than the cube of the same number can best be
represented by which of the following?
1.
2.
3.
4.
x2 + 2 ≤ x3
x2 + 2 > x3
2x – 2 ≤ x3
x2 + 2 ≥ x3
What is another way to write the following statement?
"The product of a number increased by two and that same number decreased by two is greater than
12."
1.
2.
3.
1
4.
"Eight times a number, squared, is at least five."
Which of the following best represents the statement above?
1.
2.
3.
4.
(8x)2 ≥ 5
8x2 > 5
8x2 < 5
64x ≤ 5
Which inequality is represented by the graph below?
1.
2.
3.
4.
-3  x 4
-3  x  4
-3 x 4
-3 x  4
Which graph represents the inequality -1 ≤ x < 4?
Which equation could be used to solve the given problem: If three times a number is increased by 24,
the result is 4 less than seven times the number.
1.
2.
3.
4.
3(x + 24) = 7x 4
3x + 24 = 4 7x
3x + 24 = 7x 4
27x = 7x 4
Which inequality is represented by the graph below?
2
1.
2.
3.
4.
x > -1
x < -1
x ≥ -1
x ≤ -1
Which inequality is represented by the graph below?
1.
2.
3.
4.
-2 x  3
-2 x 3
-2  x  3
-2  x 3
Which equation could represent the relationship between the x and y values shown in the
accompanying table?
1.
2.
3.
4.
y=x+2
y = x2 + 2
y = x2
y = 2x
At Ron's Rental, a person can rent a big-screen television for $10 a month plus a one-time "wear-andtear" fee of $100. At Josie's Rental, the charge is $20 a month and an additional charge of $20 for
delivery with no "wear-and-tear" fee.
If c equals the cost, write one equation representing the cost of the rental for m months at Ron's Rental
and one equation representing the cost of the rental for m months at Josie's Rental.
Ron's Rental: y =
Josie's Rental: y =
Determine in which month Josie's cost will equal Ron's cost:
m=
3
Every month, Omar buys pizzas to serve at a party for his friends. In May, he bought three more than
twice the number of pizzas he bought in April. If Omar bought 15 pizzas in May, how many pizzas did
he buy in April?
Solve for x: 8x + 9 = 5x + 6
1.
2.
3.
4.
-1
1
5
-3/13
Solve for x:
1.
2.
3.
8
-8
3
4.
-
Which diagram represents the graph of the statement x ≥ 3?
Solve for x: 6(x 2) 4x = 16
1.
2.
3.
4.
2
7
12
14
Solve for x: 0.3x = 0.01x + 2.9
4
1.
2.
3.
4.
1
0.1
10
100
Which inequality is equivalent to
1.
2.
3.
4.
?
x7
x 2
x8
x  10
Solve for x:
1.
2.
3.
4.
2
3
4
Solve for x: 0.03x 2.1 = 0.3
1.
2.
3.
4.
-6
-8
8
80
Solve for x: 4(2x 1) = 2x + 35
1.
2.
3.
4.
3.9
6.5
6
39
If x is an integer, which is the solution set of -1 ≤ x < 2?
1.
2.
3.
4.
{0, 1}
{-1, 0, 1, 2}
{0, 1, 2}
{-1, 0, 1}
Solve for x: 0.5x + 3 = 4.5
1.
-3
5
2. -5
3. 3
4. 5
Solve for x:
1.
2.
3.
4.
7
-7
63
-63
What is the value of x in the equation 4(2x + 1) = 27 + 3(2x 5)?
1.
2.
21
9
3.
4.
7
4
Solve for x: 9x 4(x 3) = 72
1.
2.
3.
4.
6
12
17
19
Which number is not a member of the solution set of the inequality 4x ≥ 18?
1.
2.
3.
4.
4.4
4.5
4.6
4.7
Solve for x: 2(x + 1) = 3(4 x)
1.
2.
3.
4.
-4
2
-2
4
If 4x + y = H, then x is equal to
1.
6
2.
3.
4.
Solve for x:
1.
2.
3.
4.
12
30
40/3
3/40
If 2x + 5 = -25 and -3m - 6 = 48, what is the product of x and m?
1.
2.
3.
4.
-270
-33
3
270
If x3 < x <
, then x could be equal to
1. 1
2. 5
3.
4.
Find all negative odd integers that satisfy the following inequality: -3x + 1 17. Write the integers in
order of least to greatest (ascending order).
If the sum of a number and four is multiplied by two, the result is 28. What is the number?
1.
2.
3.
4.
14
18
24
10
7
Vincent has cut three pieces of rope to complete a science project. Two pieces are of equal length. The
third piece is one-quarter the length of each of the others. He cut the three pieces from a rope 54 meters
long without any rope left over. Find the number of meters in each piece.
Three numbers are in the ratio 3:5:7. If the largest number is multiplied by 3, the result is 26 more than
the sum of the first and second numbers. Use an algebraic solution to find the numbers.
Ramos buys some pens and pencils. He buys seven more pens than pencils. Pens cost $0.45 each and
pencils cost $0.40 each. If he has $10 to spend, what is the greatest number of each he can buy?
The sum of two numbers is 240. The larger number is 6 less than twice the smaller. Find the numbers.
Frank is going to buy some ties at $7.50 per tie and some shirts at $18.50 per shirt. If he buys twice as
many ties as shirts and spends no more than $205, what is the greatest number of shirts he can buy?
[Assume all prices include tax.]
Two numbers are in the ratio 5:6. If the sum of the numbers is 66, find the value of the larger number.
1.
2.
3.
4.
6
24
30
36
There are 12 tomato plants in a garden. Each plant has 7 branches and each branch has 4 tomatoes
growing on it. If one-third of the tomatoes are picked, how many tomatoes were picked?
1.
2.
3.
4.
23
112
224
336
Laura goes shopping. She spends one-fourth of her money on a pair of shorts, and one-third of her
remaining money for a belt. If Laura has $42 left after these two purchases, how much money did she
have when she started shopping?
1.
2.
3.
4.
$84
$126
$144
$504
8