Solve for x. -18 x+21 > -15quad" OR "quad20 x-13 >= 27 Choose 1 answer: (A) x = 2 (B) x=-2 (C) x >= 2 D There are no solutions (E) All values of x are solutions

Solve first inequality: Solve the first inequality -18x + 21 > -15. Subtract 21 from both sides to isolate the term with x. -18x + 21 - 21 > -15 - 21 -18x > -36 Now, divide both sides by -18, remembering to reverse the inequality sign because we are dividing by a negative number. x = 27. Add 13 to both sides to isolate the term with x. 20x - 13 + 13 >= 27 + 13 20x >= 40 Now, divide both sides by 20. x >= 40 / 20 x >= 2Combine solutions: Combine the solutions from Step 1 and Step 2. The first inequality gives us x = 2. The only number that satisfies both conditions is x = 2.

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Math Problems

Precalculus

Solve rational equations

Full solution

Q. Solve for

x

\newline

-18 x+21>-15 \quad \text { OR } \quad 20 x-13 \geq 27

\newline

Choose

1

answer:

\newline

(A)

x<-2

x \geq 2

\newline

(B)

x=-2

\newline

(C)

x \geq 2

\newline

D There are no solutions

\newline

(E) All values of

x

are solutions

Solve first inequality: Solve the first inequality -18x + 21 > -15. $\newline$ Subtract $21$ from both sides to isolate the term with $x$ . $\newline$ -18x + 21 - 21 > -15 - 21 $\newline$ -18x > -36 $\newline$ Now, divide both sides by $-18$ , remembering to reverse the inequality sign because we are dividing by a negative number. $\newline$ x < \frac{-36}{-18} $\newline$ x < 2
Solve second inequality: Solve the second inequality $20x - 13 \geq 27$ . $\newline$ Add $13$ to both sides to isolate the term with $x$ . $\newline$ $20x - 13 + 13 \geq 27 + 13$ $\newline$ $20x \geq 40$ $\newline$ Now, divide both sides by $20$ . $\newline$ $x \geq \frac{40}{20}$ $\newline$ $x \geq 2$
Combine solutions: Combine the solutions from Step $1$ and Step $2$ . $\newline$ The first inequality gives us x < 2. $\newline$ The second inequality gives us $x \geq 2$ . $\newline$ The only number that satisfies both conditions is $x = 2$ .