Solve for c, 55c + 13 ≤ 75c + 39

1.	Solve for c, 55c + 13 ≤ 75c + 39
Answer» ANSWER: $55c+13\le \:75c+39\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:c\ge \:-\dfrac{13}{10}\:\\ \:\mathrm{Decimal:}&\:c\ge \:-1.3\\ \:\mathrm{Interval\:Notation:}&\:[-\dfrac{13}{10},\:\infty \:)\end{bmatrix}$ Step-by-step EXPLANATION: $55c+13\le \:75c+39$ $\gray{\mathrm{Subtract\:}13\mathrm{\:from\:both\:sides}}$ $55c+13-13\le \:75c+39-13$ $\gray{\mathrm{Simplify}}$ $55c\le \:75c+26$ $\gray{\mathrm{Subtract\:}75c\mathrm{\:from\:both\:sides}}$ $55c-75c\le \:75c+26-75c$ $\gray{\mathrm{Simplify}}$ $-20c\le \:26$ $\gray{\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}}$ $\left(-20c\right)\left(-1\right)\ge \:26\left(-1\right)$ $\gray{\mathrm{Simplify}}$ $20c\ge \:-26$ $\gray{\mathrm{Divide\:both\:sides\:by\:}20}$ $\dfrac{20c}{20}\ge \dfrac{-26}{20}$ $\gray{\mathrm{Simplify}}$ $c\ge \:-\dfrac{13}{10}$

Answer»

$55c+13\le \:75c+39\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:c\ge \:-\dfrac{13}{10}\:\\ \:\mathrm{Decimal:}&\:c\ge \:-1.3\\ \:\mathrm{Interval\:Notation:}&\:[-\dfrac{13}{10},\:\infty \:)\end{bmatrix}$