Solve for x. -15 x+4 -2 Choose 1 answer: (A) x >= -7 (B) -7 <= x < 12 (C) x < 12 D There are no solutions (E) All values of x are solutions

Solve the first inequality: First, let's solve the inequality -15x + 4 ≤ 109. Subtract 4 from both sides to isolate the term with x. -15x + 4 - 4 ≤ 109 - 4 -15x ≤ 105 Now, divide both sides by -15, remembering to reverse the inequality sign because we are dividing by a negative number. x ≥ -7Solve the second inequality: Next, let's solve the inequality -6x + 70 > -2. Subtract 70 from both sides to isolate the term with x. -6x + 70 - 70 > -2 - 70 -6x > -72 Now, divide both sides by -6, again remembering to reverse the inequality sign because we are dividing by a negative number. x < 12Intersection of the inequalities: Now we have two inequalities that define the solution set for x: x ≥ -7 and x < 12. The solution set for x is the intersection of these two inequalities, which is the set of all x that satisfy both conditions simultaneously. Therefore, the solution set for x is -7 ≤ x < 12.

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Solve for
x.

-15 x+4 <= 109quad" OR "quad-6x+70 > -2
Choose 1 answer:
(A)
x >= -7
(B)
-7 <= x < 12
(C)
x < 12
D There are no solutions
(E) All values of
x are solutions

Solve for $x$ . $\newline$ -15 x+4 \leq 109 \quad \text { OR } \quad-6 x+70>-2 $\newline$ Choose $1$ answer: $\newline$ (A) $x \geq-7$ $\newline$ (B) -7 \leq x<12 $\newline$ (C) x<12 $\newline$ 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

-15 x+4 \leq 109 \quad \text { OR } \quad-6 x+70>-2

\newline

Choose

1

answer:

\newline

(A)

x \geq-7

\newline

(B)

-7 \leq x<12

\newline

(C)

x<12

\newline

D There are no solutions

\newline

(E) All values of

x

are solutions

Solve the first inequality: First, let's solve the inequality $-15x + 4 \leq 109$ . $\newline$ Subtract $4$ from both sides to isolate the term with $x$ . $\newline$ $-15x + 4 - 4 \leq 109 - 4$ $\newline$ $-15x \leq 105$ $\newline$ Now, divide both sides by $-15$ , remembering to reverse the inequality sign because we are dividing by a negative number. $\newline$ $x \geq -7$
Solve the second inequality: Next, let's solve the inequality -6x + 70 > -2. $\newline$ Subtract $70$ from both sides to isolate the term with $x$ . $\newline$ -6x + 70 - 70 > -2 - 70 $\newline$ -6x > -72 $\newline$ Now, divide both sides by $-6$ , again remembering to reverse the inequality sign because we are dividing by a negative number. $\newline$ x < 12
Intersection of the inequalities: Now we have two inequalities that define the solution set for x: $\newline$ $x \geq -7$ and x < 12. $\newline$ The solution set for x is the intersection of these two inequalities, which is the set of all x that satisfy both conditions simultaneously. $\newline$ Therefore, the solution set for x is -7 \leq x < 12.