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Solve the compound inequality 2x − 3 < 7 and 5 − x ≤ 8. A. x ≥ 3 and x < 2 B. x ≥ 3 and x < 5 C. x ≥ −3 and x < 2 D. x ≥ −3 and x < 5

User PhilMasteG
by
8.0k points

2 Answers

4 votes

The solution to the compound inequality is
\(x \geq -3\) and x < 5, which is represented by option D.

Let's solve the compound inequality step by step:

1. 2x - 3 < 7

Add 3 to both sides:

2x < 10

Divide by 2 (since the coefficient of x is 2 and we want to isolate x):

x < 5

2.
\(5 - x \leq 8\)

Subtract 5 from both sides:


\(-x \leq 3\)

Multiply by -1 (note that when multiplying or dividing by a negative number, the inequality sign flips):


\(x \geq -3\)

So, the solutions to the compound inequality are x < 5 and
\(x \geq -3\).

Now, looking at the answer choices:

C.
\(x \geq -3\) and x < 2 – Incorrect

D.
\(x \geq -3\) and x < 5 – Correct

Therefore, the correct answer is D.
\(x \geq -3\) and \(x < 5\).

User Viktor Vostrikov
by
7.4k points
3 votes

Given:

The compound inequality
2x-3 < 7 and
5-x \leq 8.

To find:

The solution for the given compound inequality

Solution:

We have, compound inequality
2x-3 < 7 and
5-x \leq 8.

For
2x-3 < 7,

Add 3 on both sides.


2x < 7+3


2x < 10

Divide 2 on both sides.


x< 5 ...(i)

For
5-x \leq 8,

Subtract 5 from both sides.


-x \leq 8-5


-x \leq 3

Divide both sides by -1. So, the sign of inequality is changed.


x \geq -3 ...(ii)

Using (i) and (ii), we get the solution of given compound inequality as


x \geq -3 and
x< 5

Therefore, the correct option is D.

User Seveninstl
by
8.0k points

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