Which set expresses the solution to the compound inequality -2 _< 2x + 1/3 - 4 < 1?

Answer 1

To find the solution to the compound inequality -2 ≤ 2x + 1/3 - 4 < 1, we first need to isolate x.

We can start by adding 4 to all parts of the compound inequality:

-2 + 4 ≤ 2x + 1/3 - 4 + 4 < 1 + 4

This simplifies to:

2 ≤ 2x + 1/3 < 5

Next, we can subtract 1/3 from all parts of the compound inequality:

2 - 1/3 ≤ 2x + 1/3 - 1/3 < 5 - 1/3

This simplifies to:

5/3 ≤ 2x < 14/3

Finally, we can divide all parts of the compound inequality by 2 to solve for x:

(5/3)/2 ≤ (2x)/2 < (14/3)/2

This simplifies to:

5/6 ≤ x < 7/3

Therefore, the solution to the compound inequality is expressed as the set:

{x | 5/6 ≤ x < 7/3}

Answer 2

Which set expresses the solution to the compund inequility -2 _< 2x + 1/3 - 4 < 1?
A. { x : 3 _< x <7}
B. { x : 5/2 _< x < 1}
C. { x : -3/2 _< x < 1 }
D. { x : 5/2 _< x < 7 }

Answer 3

To find the solution to the compound inequality -2 ≤ 2x + 1/3 - 4 < 1, let's solve each inequality separately.

First, let's solve -2 ≤ 2x + 1/3 - 4. We can start by adding 4 to both sides of the inequality:

-2 + 4 ≤ 2x + 1/3 - 4 + 4

2 ≤ 2x + 1/3

Next, let's isolate 2x by subtracting 1/3 from both sides:

2 - 1/3 ≤ 2x + 1/3 - 1/3

2 - 1/3 ≤ 2x

6/3 - 1/3 ≤ 2x

5/3 ≤ 2x

Now, let's solve 2x + 1/3 - 4 < 1. We can start by adding 4 to both sides of the inequality:

2x + 1/3 - 4 + 4 < 1 + 4

2x + 1/3 < 5

Now, let's isolate 2x by subtracting 1/3 from both sides:

2x + 1/3 - 1/3 < 5 - 1/3

2x < 14/3

Finally, let's isolate x by dividing both sides by 2:

(2x)/2 < (14/3)/2

x < 7/3

Combining the results, we have:

5/3 ≤ x < 7/3

Therefore, the correct answer is:

D. { x : 5/2 _< x < 7 }

Answer 4

What property of equality is displayed in step 3 in the solving of 9m + 4 - 7m = 5m +7/3?

Answer 5

The property of equality displayed in step 3 of the equation 9m + 4 - 7m = 5m + 7/3 is the addition property of equality.

In this step, we are combining like terms by adding the variable terms (9m and -7m) on the left side of the equation and the constant terms (4) on the left side of the equation.

Using the addition property of equality, we can simplify the equation to:

2m + 4 = 5m + 7/3

Answer 6

Which linear equation has the same solution set as 9d/4 + 3 - 2d = -2 (3 + d) ?

A. 4w - 2 (7 - 3w) = w/3 - 6
B. 14 = 7/4 x - 19/4 + 2x
C. 35 - 15b = 95
D. 3x/5 - 10 = -7

Answer 7

To find the linear equation that has the same solution set as 9d/4 + 3 - 2d = -2(3 + d), we need to simplify the given equation and compare it to the options.

Let's simplify the given equation step by step:

9d/4 + 3 - 2d = -2(3 + d)

First, distribute the -2 to the terms in the parentheses:

9d/4 + 3 - 2d = -6 - 2d

Now, let's combine like terms by subtracting 2d from both sides:

9d/4 + 3 - 2d - (-2d) = -2d - (-2d) - 6

This simplifies to:

9d/4 + 3 = -6

Next, let's subtract 3 from both sides:

9d/4 + 3 - 3 = -6 - 3

This simplifies to:

9d/4 = -9

To isolate d, let's multiply both sides by 4/9:

(4/9)(9d/4) = (4/9)(-9)

This simplifies to:

d = -4

Now, let's compare the solution, d = -4, with the options:

A. 4w - 2(7 - 3w) = w/3 - 6: This equation is not equivalent to the given equation and does not have the same solution set.

B. 14 = 7/4x - 19/4 + 2x: This equation is not equivalent to the given equation and does not have the same solution set.

C. 35 - 15b = 95: This equation is not equivalent to the given equation and does not have the same solution set.

D. 3x/5 - 10 = -7: This equation does not have the same solution set as the given equation.

None of the options have the same solution set as the given equation 9d/4 + 3 - 2d = -2(3 + d).