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Given the follow inequality, which of the following presents a range of possible answers for the inequality: –3 < 3x + 2 ≤ 3.5
( –2, 2)
(–1,1)
(–1, ½)
(½, 1)
(–3, 1/2)
Explanation
If you plug in the outer limits of the given ranges, (–1, ½) is the only combination that fits within the given equation. It is important to remember that "<" means “less than,” and "≤" means “less than or equal.” For example, if you answered (–2,2), plugging in 2 would make the the expression equal 8, which is greater than 3.5. And plugging in –2 for x would make the expression equal –4, which is less than –3, not greater. However, plugging in the correct answer (–1, ½) gives you –1 as your lower limit and 3.5 as your upper limit, which satisfies the equation. Both limits of the data set must satisfy the equation.
Given the follow inequality, which of the following presents a range of possible answers for the inequality: –3 < 3x + 2 ≤ 3.5
( –2, 2)
(–1,1)
(–1, ½)
(½, 1)
(–3, 1/2)
Explanation
If you plug in the outer limits of the given ranges, (–1, ½) is the only combination that fits within the given equation. It is important to remember that "<" means “less than,” and "≤" means “less than or equal.” For example, if you answered (–2,2), plugging in 2 would make the the expression equal 8, which is greater than 3.5. And plugging in –2 for x would make the expression equal –4, which is less than –3, not greater. However, plugging in the correct answer (–1, ½) gives you –1 as your lower limit and 3.5 as your upper limit, which satisfies the equation. Both limits of the data set must satisfy the equation.
When you multiply a number by 5 and then subtract 23, the result is the same as when you multiplied the same number by 3 then added 3. What is the number?
5
6
7
10
13
Explanation
You set up the equation 5x – 23 = 3x + 3, then solve for x, giving you 13.
When you multiply a number by 5 and then subtract 23, the result is the same as when you multiplied the same number by 3 then added 3. What is the number?
5
6
7
10
13
Explanation
You set up the equation 5x – 23 = 3x + 3, then solve for x, giving you 13.
What is the product of the two values of 
Explanation
First, solve for the values of x by factoring.
Then, multiply the solutions to obtain the product.
What is the product of the two values of
Explanation
First, solve for the values of x by factoring.
Then, multiply the solutions to obtain the product.
When you divide a number by 3 and then add 2, the result is the same as when you multiply the same number by 2 then subtract 23. What is the number?
2
3
15
7
9
Explanation
You set up the equation and you get: (x/3) + 2 = 2_x –_ 23.
Add 23 to both sides: (x/3) + 25 = 2_x_
Multiply both sides by 3: x + 75 = 6_x_
Subtract x from both sides: 75 = 5_x_
Divide by 5 and get x = 15
When you divide a number by 3 and then add 2, the result is the same as when you multiply the same number by 2 then subtract 23. What is the number?
2
3
15
7
9
Explanation
You set up the equation and you get: (x/3) + 2 = 2_x –_ 23.
Add 23 to both sides: (x/3) + 25 = 2_x_
Multiply both sides by 3: x + 75 = 6_x_
Subtract x from both sides: 75 = 5_x_
Divide by 5 and get x = 15
|2x – 25| – 3 = 7. There are two solutions to this problem. What is the sum of those solutions?
25
7.5
10
17
Explanation
First, simplify the equation so the absolute value is all that remains on the left side of the equation:
|2_x_ – 25| = 10
Now create two equalities, one for 10 and one for –10.
2_x_ – 25 = 10 and 2_x_ – 25 = –10
2_x_ = 35 and 2_x_ = 15
x = 17.5 and x = 7.5
The two solutions are 7.5 and 17.5. 17.5 + 7.5 = 25
|2x – 25| – 3 = 7. There are two solutions to this problem. What is the sum of those solutions?
25
7.5
10
17
Explanation
First, simplify the equation so the absolute value is all that remains on the left side of the equation:
|2_x_ – 25| = 10
Now create two equalities, one for 10 and one for –10.
2_x_ – 25 = 10 and 2_x_ – 25 = –10
2_x_ = 35 and 2_x_ = 15
x = 17.5 and x = 7.5
The two solutions are 7.5 and 17.5. 17.5 + 7.5 = 25