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Solve for $u$ . $\newline$ $|-u| > 14$ $\newline$ Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$ . Use integers, proper fractions, or improper fractions in simplest form. $\newline$ ______

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Solve absolute value inequalities

Full solution

Q. Solve for

u

.

\newline

|-u| > 14

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

or

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

______

Understand absolute value: We have the inequality: $\newline$ $|-u| > 14$ $\newline$ First, we need to understand the absolute value inequality. The absolute value of a number is always non-negative, so $|-u| > 14$ means that the value of $-u$ is either greater than $14$ or less than $-14$ .
Split into two inequalities: Now we can split the inequality into two separate inequalities to remove the absolute value: $-u > 14$ or $-u < -14$
Solve first inequality: Next, we solve each inequality for $u$ . Starting with the first inequality: $-u > 14$ Multiply both sides by $-1$ (remember to flip the inequality sign when multiplying or dividing by a negative number): $u < -14$
Solve second inequality: Now, we solve the second inequality: $\newline$ $-u < -14$ $\newline$ Multiply both sides by $-1$ (again, remember to flip the inequality sign): $\newline$ $u > 14$
Combine both inequalities: Combining both inequalities, we get the compound inequality: $\newline$ $u < -14$ or $u > 14$ $\newline$ This is the solution to the original problem.

More problems from Solve absolute value inequalities

Question

u

\newline

|u| - 4 \geq 6

\newline

\newline

Write a compound inequality like

1 < x < 3

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\newline

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Question

9 \frac{7}{8}

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Question

\newline

Solve the system of equations.

\newline

\begin{array}{l} y=22 x-38 \\ y=x^{2}+11 x-14 \end{array}

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Write the coordinates in exact form. Simplify all fractions and radicals.

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\newline

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\newline

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\newline

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Question

1,2,3,4,5

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\newline

The probability that the three-digit number is even and greater than

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\square

\newline

(Type an integer or a simplified fraction.)

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Use benchmark fractions to estimate sums and differences less than or gremet than

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\newline

\begin{array}{l} \frac{7}{8}+\frac{5}{10} \\ 1 \frac{5}{8}-\frac{5}{6} \\ \frac{10}{10}-\frac{2}{3} \\ \frac{1}{2}+\frac{2}{3} \\ \frac{5}{12}+\frac{1}{4} \\ 1 \frac{1}{6}+\frac{7}{8} \\ \end{array}

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Question

Eric is sorting pencils into boxes. He put

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\newline

\newline

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Posted 1 month ago

Question

Given the definitions of

f(x)

g(x)

below, find the value of

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\newline

\begin{array}{l} f(x)=-5 x+3 \\ g(x)=2 x^{2}+5 x-14 \end{array}

\newline

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Question

t

\newline

|t + 8| \leq 4

\newline

Write a compound inequality like

1 < x < 3

x < 1

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

Posted 1 month ago