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$Solve for d. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. -38 d-57 >= -19 d+76 ◻$

Solve for $d$ . $\newline$ Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $\newline$ $-38 d-57 \geq-19 d+76$ $\newline$ $\square$

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Solve polynomial equations

Full solution

Q. Solve for

d

.

\newline

Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

\newline

-38 d-57 \geq-19 d+76

\newline

\square

Move terms to one side: First, we want to isolate the variable $d$ on one side of the inequality. To do this, we can start by adding $38d$ to both sides to move all the $d$ terms to one side. $\newline$ $-38d - 57 + 38d \geq -19d + 76 + 38d$ $\newline$ This simplifies to: $\newline$ $-57 \geq 19d + 76$
Isolate term with d: Next, we subtract $76$ from both sides to isolate the term with $d$ .
$-57 - 76 \geq 19d + 76 - 76$
This simplifies to:
$-133 \geq 19d$
Solve for d: Now, we divide both sides by $19$ to solve for $d$ . Since we are dividing by a positive number, the direction of the inequality does not change. $\newline$ $-133 / 19 \geq 19d / 19$ $\newline$ This simplifies to: $\newline$ $-7 \geq d$ $\newline$ Or equivalently: $\newline$ $d \leq -7$

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