Solve for x. 5x-4 >= 12quad OR quad12 x+5 = (16)/(5) or x = -(3)/(4) (D) There are no solutions (E) All values of x are solutions

Solve first inequality: Solve the first inequality 5x - 4 ≥ 12. Add 4 to both sides to isolate the term with x on one side. 5x - 4 + 4 ≥ 12 + 4 5x ≥ 16 Now, divide both sides by 5 to solve for x. x ≥ 16/5Solve second inequality: Solve the second inequality 12x + 5 ≤ -4. Subtract 5 from both sides to isolate the term with x on one side. 12x + 5 - 5 ≤ -4 - 5 12x ≤ -9 Now, divide both sides by 12 to solve for x. x ≤ -9/12 Simplify the fraction -9/12 to -3/4. x ≤ -3/4Combine solutions: Combine the solutions from Step 1 and Step 2. The solution to the system of inequalities is the union of the individual solutions. x ≥ 16/5 or x ≤ -3/4

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Precalculus

Solve rational equations

Full solution

Q. Solve for

x

\newline

5 x-4 \geq 12 \quad

\quad 12 x+5 \leq-4

\newline

Choose

1

answer:

\newline

(A)

x \geq \frac{16}{5}

x \leq-\frac{3}{4}

\newline

(B)

x \leq \frac{16}{5}

\newline

(C)

x \geq-\frac{3}{4}

\newline

(D) There are no solutions

\newline

(E) All values of

x

are solutions

Solve first inequality: Solve the first inequality $5x - 4 \geq 12$ . $\newline$ Add $4$ to both sides to isolate the term with $x$ on one side. $\newline$ $5x - 4 + 4 \geq 12 + 4$ $\newline$ $5x \geq 16$ $\newline$ Now, divide both sides by $5$ to solve for $x$ . $\newline$ $x \geq \frac{16}{5}$
Solve second inequality: Solve the second inequality $12x + 5 \leq -4$ .
Subtract $5$ from both sides to isolate the term with $x$ on one side.
$12x + 5 - 5 \leq -4 - 5$
$12x \leq -9$
Now, divide both sides by $12$ to solve for $x$ .
$x \leq -\frac{9}{12}$
Simplify the fraction $-\frac{9}{12}$ to $-\frac{3}{4}$ .
$5$ $0$
Combine solutions: Combine the solutions from Step $1$ and Step $2$ . $\newline$ The solution to the system of inequalities is the union of the individual solutions. $\newline$ $x \geq \frac{16}{5}$ or $x \leq -\frac{3}{4}$