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Solve for $w$ . $\newline$ $|-2w| > 14$ $\newline$ 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

w

.

\newline

|-2w| > 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

______

Given Inequality: We have the inequality: $\newline$ $|-2w| > 14$ $\newline$ First, we need to solve for $|2w|$ . $\newline$ $|-2w| > 14$ $\newline$ This means that the absolute value of $-2w$ is greater than $14$ .
Split into Two Cases: The absolute value inequality $|-2w| > 14$ can be split into two separate inequalities because if the absolute value of a number is greater than $14$ , the number itself can either be greater than $14$ or less than $-14$ . $\newline$ So we have two cases: $\newline$ $-2w > 14$ or $-2w < -14$
Solve First Inequality: Let's solve the first inequality: $\newline$ $-2w > 14$ $\newline$ To isolate $w$ , we divide both sides by $-2$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $w < -7$
Solve Second Inequality: Now let's solve the second inequality: $\newline$ $-2w < -14$ $\newline$ Again, we divide both sides by $-2$ , and the inequality sign reverses. $\newline$ $w > 7$
Combine Inequalities: Combining both inequalities, we get the compound inequality: $\newline$ $w < -7$ or $w > 7$ $\newline$ 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

x < 1

x > 3

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

\newline

Posted 2 months ago

Question

9 \frac{7}{8}

into an improper fraction.

\newline

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f(x)=\left\{\begin{array}{lll} -4 x & \text { for } & x<-1 \\ -x+1 & \text { for } & -1 \leq x \leq 3 \\ -2 x+8 & \text { for } & x>3 \end{array}\right.

\newline

f(3)

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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}

\newline

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

\newline

\begin{array}{l} (-,-) \\ (-,-) \end{array}

\newline

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\newline

\frac{2}{5}

\newline

\frac{5}{2}

\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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pencils in the second box,

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pencils in the third box, and

31

pencils in the fourth box. What kind of sequence is this?

\newline

\newline

\newline

\newline

\newline

Posted 1 month ago

Question

Given the definitions of

f(x)

g(x)

below, find the value of

g(f(2))

\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