Solve for x. -6x+14 7 (B) -1 <= x < 7 (C) x < 7 (D) There are no solutions (E) All values of x are solutions

Solving the first inequality: First, let's solve the first inequality -6x + 14 7Solving the second inequality: Next, let's solve the second inequality 3x + 28 ≤ 25. Subtract 28 from both sides to isolate the term with x. 3x + 28 - 28 ≤ 25 - 28 3x ≤ -3 Now, divide both sides by 3 to solve for x. x ≤ -1Considering the two inequalities: Now we have two inequalities to consider: x > 7 from the first inequality and x ≤ -1 from the second inequality. These two inequalities do not overlap; there is no value of x that can satisfy both conditions simultaneously. Therefore, there are no solutions to the system of inequalities.

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Solve for
x.

-6x+14 < -28quad AND
quad3x+28 <= 25
Choose 1 answer:
(A)
x <= -1 or
x > 7
(B)
-1 <= x < 7
(C)
x < 7
(D) There are no solutions
(E) All values of
x are solutions

Solve for $x$ . $\newline$ -6 x+14<-28 \quad AND $\quad 3 x+28 \leq 25$ $\newline$ Choose $1$ answer: $\newline$ (A) $x \leq-1$ or x>7 $\newline$ (B) -1 \leq x<7 $\newline$ (C) x<7 $\newline$ (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

-6 x+14<-28 \quad

AND

\quad 3 x+28 \leq 25

\newline

Choose

1

answer:

\newline

(A)

x \leq-1

x>7

\newline

(B)

-1 \leq x<7

\newline

(C)

x<7

\newline

(D) There are no solutions

\newline

(E) All values of

x

are solutions

Solving the first inequality: First, let's solve the first inequality -6x + 14 < -28. $\newline$ Subtract $14$ from both sides to isolate the term with $x$ . $\newline$ -6x + 14 - 14 < -28 - 14 $\newline$ -6x < -42 $\newline$ Now, divide both sides by $-6$ , remembering to reverse the inequality sign because we are dividing by a negative number. $\newline$ x > 7
Solving the second inequality: Next, let's solve the second inequality $3x + 28 \leq 25$ . $\newline$ Subtract $28$ from both sides to isolate the term with $x$ . $\newline$ $3x + 28 - 28 \leq 25 - 28$ $\newline$ $3x \leq -3$ $\newline$ Now, divide both sides by $3$ to solve for $x$ . $\newline$ $x \leq -1$
Considering the two inequalities: Now we have two inequalities to consider: x > 7 from the first inequality and $x \leq -1$ from the second inequality. $\newline$ These two inequalities do not overlap; there is no value of $x$ that can satisfy both conditions simultaneously. $\newline$ Therefore, there are no solutions to the system of inequalities.