Solve for x. -8x+14 >= 60quad" OR "quad-4x+50 -2 (B) x -2 (D) There are no solutions (E) All values of x are solutions

Solving the first inequality: First, let's solve the inequality -8x + 14 ≥ 60. Subtract 14 from both sides to isolate the term with x. -8x + 14 - 14 ≥ 60 - 14 -8x ≥ 46 Now, divide both sides by -8. Remember that dividing by a negative number reverses the inequality sign. -8x / -8 ≤ 46 / -8 x ≤ -46 / 8 x ≤ -23 / 4Solving the second inequality: Next, let's solve the inequality -4x + 50 8 / -4 x > -2Combining the inequalities: Now we have two inequalities: x ≤ -23 / 4 x > -2 These two inequalities represent the solution set for x. The first inequality allows any x that is less than or equal to -23/4, and the second inequality allows any x that is greater than -2.Finding the solution to the system: To find the solution to the system, we need to find the intersection of the two solution sets. However, since -23/4 is less than -2, there is no overlap between the two sets. Therefore, the solution to the system is the union of the two sets, which means x can be any number less than or equal to -23/4 or greater than -2.

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Solve for
x.

-8x+14 >= 60quad" OR "quad-4x+50 < 58
Choose 1 answer:
A
x <= -(23)/(4) or
x > -2
(B)
x <= -(23)/(4)
(C)
x > -2
(D) There are no solutions
(E) All values of
x are solutions

Solve for $x$ . $\newline$ -8 x+14 \geq 60 \quad \text { OR } \quad-4 x+50<58 $\newline$ Choose $1$ answer: $\newline$ A $x \leq-\frac{23}{4}$ or x>-2 $\newline$ (B) $x \leq-\frac{23}{4}$ $\newline$ (C) x>-2 $\newline$ (D) There are no solutions $\newline$ (E) All values of $x$ are solutions

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Math Problems

Algebra 1

Is (x, y) a solution to the system of linear inequalities?

Full solution

Q. Solve for

x

\newline

-8 x+14 \geq 60 \quad \text { OR } \quad-4 x+50<58

\newline

Choose

1

answer:

\newline

x \leq-\frac{23}{4}

x>-2

\newline

(B)

x \leq-\frac{23}{4}

\newline

(C)

x>-2

\newline

(D) There are no solutions

\newline

(E) All values of

x

are solutions

Solving the first inequality: First, let's solve the inequality $-8x + 14 \geq 60$ . $\newline$ Subtract $14$ from both sides to isolate the term with $x$ . $\newline$ $-8x + 14 - 14 \geq 60 - 14$ $\newline$ $-8x \geq 46$ $\newline$ Now, divide both sides by $-8$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $-8x / -8 \leq 46 / -8$ $\newline$ $x \leq -46 / 8$ $\newline$ $x \leq -23 / 4$
Solving the second inequality: Next, let's solve the inequality -4x + 50 < 58.
Subtract $50$ from both sides to isolate the term with $x$ .
-4x + 50 - 50 < 58 - 50
-4x < 8
Now, divide both sides by $-4$ . Again, remember that dividing by a negative number reverses the inequality sign.
\frac{-4x}{-4} > \frac{8}{-4}
x > -2
Combining the inequalities: Now we have two inequalities: $\newline$ $x \leq -\frac{23}{4}$ $\newline$ x > -2 $\newline$ These two inequalities represent the solution set for $x$ . The first inequality allows any $x$ that is less than or equal to $-\frac{23}{4}$ , and the second inequality allows any $x$ that is greater than $-2$ .
Finding the solution to the system: To find the solution to the system, we need to find the intersection of the two solution sets. However, since $-\frac{23}{4}$ is less than $-2$ , there is no overlap between the two sets. Therefore, the solution to the system is the union of the two sets, which means $x$ can be any number less than or equal to $-\frac{23}{4}$ or greater than $-2$ .