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Solve for $w$ . $\newline$ $|w| + 7 > 17$ $\newline$ 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

w

.

\newline

|w| + 7 > 17

\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

______

Isolate absolute value: We have the inequality: $\newline$ $|w| + 7 > 17$ $\newline$ First, we isolate $|w|$ by subtracting $7$ from both sides of the inequality. $\newline$ $|w| + 7 - 7 > 17 - 7$ $\newline$ $|w| > 10$
Interpret absolute value: Now we interpret the absolute value inequality $|w| > 10$ . This means that $w$ is either greater than $10$ or less than $-10$ . So we can write two separate inequalities: $w > 10$ or $w < -10$
Final compound inequality: We now have the compound inequality that represents the solution to the original problem: $\newline$ $w > 10$ or $w < -10$ $\newline$ This is the final answer in the form of a compound inequality.

More problems from Solve absolute value inequalities

Question

u

\newline

|u| - 4 \geq 6

\newline

\newline

Write a compound inequality like

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\newline

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Question

9 \frac{7}{8}

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\newline

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\newline

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Question

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\newline

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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

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\newline

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Posted 1 month ago

Question

Given the definitions of

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g(x)

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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

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

\newline

Posted 1 month ago