Question

Solve for xxx.3x-8\leq 23\quad \maroonC{\text{ OR }} \quad -4x+26\geq63x−8≤23 OR −4x+26≥63, x, minus, 8, is less than or equal to, 23, start color #ed5fa6, start text, space, O, R, space, end text, end color #ed5fa6, minus, 4, x, plus, 26, is greater than or equal to, 6Choose 1 answer:Choose 1 answer:(Choice A)Ax\leq \dfrac{31}3x≤331​x, is less than or equal to, start fraction, 31, divided by, 3, end fraction(Choice B)Bx\leq5x≤5x, is less than or equal to, 5(Choice C)C5 \leq x \leq \dfrac{31}{3}5≤x≤331​5, is less than or equal to, x, is less than or equal to, start fraction, 31, divided by, 3, end fraction(Choice D)DThere are no solutions(Choice E)E

Answer 1

Starting with the first part of the inequality:

3x - 8 ≤ 23

Add 8 to both sides to isolate 3x:

3x ≤ 23 + 8

3x ≤ 31

Now, divide both sides by 3 to solve for x:

x ≤ 31 / 3

So, the first part of the inequality gives us:

x ≤ 31/3

Now, let's solve the second part of the inequality:

-4x + 26 ≥ 6

Subtract 26 from both sides:

-4x ≥ 6 - 26

-4x ≥ -20

Divide both sides by -4. Remember that when you divide or multiply an inequality by a negative number, you need to reverse the inequality sign:

x ≤ -20 / -4

x ≤ 5

So, the second part of the inequality gives us:

x ≤ 5

Now, combining both parts, we have:

x ≤ 31/3 OR x ≤ 5

The correct choice is (Choice C):

5 ≤ x ≤ 31/3