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Solve for
x.

-9x+5 < 17quad AND
quad13 x+25 < -1
Choose 1 answer:
(A)
x < -2 or
x > -(4)/(3)
(B)
x < -2
(C)
x > -(4)/(3)
(D) There are no solutions
(E) All values of
x are solutions

Solve for $x$ . $\newline$ -9 x+5<17 \quad AND \quad 13 x+25<-1 $\newline$ Choose $1$ answer: $\newline$ (A) x<-2 or x>-\frac{4}{3} $\newline$ (B) x<-2 $\newline$ (C) x>-\frac{4}{3} $\newline$ (D) There are no solutions $\newline$ (E) All values of $x$ are solutions

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

Full solution

Q. Solve for

x

.

\newline

-9 x+5<17 \quad

AND

\quad 13 x+25<-1

\newline

Choose

1

answer:

\newline

(A)

x<-2

or

x>-\frac{4}{3}

\newline

(B)

x<-2

\newline

(C)

x>-\frac{4}{3}

\newline

(D) There are no solutions

\newline

(E) All values of

x

are solutions

Solve first inequality: First, let's solve the inequality -9x + 5 < 17. $\newline$ Subtract $5$ from both sides to isolate the term with $x$ . $\newline$ -9x + 5 - 5 < 17 - 5 $\newline$ -9x < 12 $\newline$ Now, divide both sides by $-9$ , remembering to reverse the inequality sign because we are dividing by a negative number. $\newline$ x > -\frac{12}{-9} $\newline$ x > \frac{4}{3}
Solve second inequality: Next, let's solve the second inequality 13x + 25 < -1. $\newline$ Subtract $25$ from both sides to isolate the term with $x$ . $\newline$ 13x + 25 - 25 < -1 - 25 $\newline$ 13x < -26 $\newline$ Now, divide both sides by $13$ to solve for $x$ . $\newline$ x < -26 / 13 $\newline$ x < -2
Combine inequalities and find solution: Now we have two inequalities to combine into one solution set: $\newline$ x > \frac{4}{3} and x < -2. $\newline$ However, these two inequalities do not overlap; there is no number that is both greater than $\frac{4}{3}$ and less than $-2$ . Therefore, there is no solution to the system of inequalities.

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