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Solve for $s$ . $\newline$ $|s| - 3 \leq 11$ $\newline$ 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

s

.

\newline

|s| - 3 \leq 11

\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 $|s| - 3 \leq 11$ . First, we need to isolate the absolute value term $|s|$ on one side of the inequality. $\newline$ $|s| - 3 + 3 \leq 11 + 3$ $\newline$ $|s| \leq 14$
Interpret absolute value inequality: Now that we have isolated $\lvert s \rvert$ , we can interpret the absolute value inequality. The inequality $\lvert s \rvert \leq 14$ means that $s$ is within a distance of $14$ from $0$ on the number line. $\newline$ This gives us two inequalities: $\newline$ $s \leq 14$ and $-s \leq 14$
Multiply by $-1$ : The second inequality, $-s \leq 14$ , can be multiplied by $-1$ to get $s \geq -14$ . Remember that multiplying or dividing an inequality by a negative number reverses the inequality sign. $\newline$ $s \geq -14$
Combine inequalities: Combining the two inequalities from the previous steps, we get a compound inequality that represents the solution for $s$ : $-14 \leq s \leq 14$

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

\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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\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

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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)

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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