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Solve for $u$ . $\newline$ $6.4u < 3.84 + 6.8u$ $\newline$ $\newline$ Write your answer with $u$ first, followed by an inequality symbol. $\newline$ ______ $\newline$

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Solve inequalities with decimals: variables on both sides

Full solution

Q. Solve for

u

.

\newline

6.4u < 3.84 + 6.8u

\newline

\newline

Write your answer with

u

first, followed by an inequality symbol.

\newline

______

\newline

Isolate variable u: First, we want to isolate the variable u on one side of the inequality. To do this, we will subtract $6.4u$ from both sides of the inequality. $\newline$ $6.4u < 3.84 + 6.8u$ $\newline$ $6.4u - 6.4u < 3.84 + 6.8u - 6.4u$ $\newline$ $0 < 3.84 + 0.4u$
Subtract $3$ . $84$ : Now, we will subtract $3.84$ from both sides to isolate the term with the variable $u$ . $\newline$ $0 - 3.84 < 3.84 + 0.4u - 3.84$ $\newline$ $-3.84 < 0.4u$
Divide by $0$ . $4$ : Next, we will divide both sides by $0.4$ to solve for $u$ . Remember that since we are dividing by a positive number, the direction of the inequality will not change. $\newline$ $-3.84 / 0.4 < 0.4u / 0.4$ $\newline$ $-9.6 < u$

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