All categories

4 years ago

Solve the inequality |x| < 5.

Mathematics

1 answer:

Nuetrik [128]4 years ago

8 0

<h2>Hello!</h2>

The answer is:

{-5<x<5}

To solve the problem, we need to remember how Absolute Value Functions behave, when we have this type of function, related to an inequality, the solution will be between two values.

We are given the inequality:

$|x|$

So, we know that "x" will be between -5 and 5:

$-5$

Hence, the solution of the given inequality will be:

(-5,5) or {-5<x<5}

Have a nice day!

You might be interested in

Write an equation for the line whose slope is 7/2 and which contains the point (-12,-9)

blagie [28]

Slope-intercept form:

y = mx + b "m" is the slope, "b" is the y-intercept (the y value when x = 0)

Since you know m = 7/2, plug it into the equation

y = 7/2x + b

To find "b", plug in (-12,-9) into the equation

y = 7/2x + b

-9 = 7/2(-12) + b

-9 = -84/2 + b

-9 = -42 + b Add 42 on both sides

33 = b

$y=\frac{7}{2}x+33$

(if you're not suppose to use slope-intercept form)

Point-slope form:

y - y₁ = m(x - x₁)

m = 7/2

(x₁ , y₁) = (-12,-9)

Plug this into the equation

y - y₁ = m(x - x₁)

y - (-9) = 7/2(x - (-12))

$y+9=\frac{7}{2}(x+12)$

5 0

3 years ago

A toy rocket is launched from the top of a building 135 feet tall at an initial velocity of 167 feet per second. Give the functi

Cerrena [4.2K]

Answer:

h(t) = = -16t^2 + 167t + 135

Step-by-step explanation:

This is an equation of motion of an object umder a constant acceleration(here it is the acceleration due to gravity);

h(t) = = -16t^2 + 167t + 135.

Note: t is the time in seconds and h is the height in feet at time t.

3 0

3 years ago

Simplify this expression: 5 + 2b - 2

Stells [14]

Answer: 2b+3

Combine like terms which are 5 and -2

5 0

3 years ago

Read 2 more answers

The quotient of a number y and -3.6 is less than 6.5 <br><br> (written as an inequality)

elena-14-01-66 [18.8K]

Answer:

$\frac{y}{-3.6}$ < 6.5

7 0

3 years ago

Simplify the expression below.<br> 12b + 86 + 5b<br> 0 25 + b<br> O 25(3b)<br> 25b<br> 3b

Alja [10]

(1): "^-5" was replaced by "^(-5)". 3 more similar replacement(s)

STEP

Equation at the end of step 1

((25•(b-1))•(c-3))

(((12•(b4))•(c-6))•——————————————————)•((2•5b(-5))•c)

((15•(b3))•(c4))

STEP

Equation at the end of step

((25•(b-1))•(c-3))

(((12•(b4))•(c-6))•——————————————————)•(2•5b(-5)c)

((3•5b3)•c4)

STEP

Equation at the end of step

(52b(-1)•c(-3))

(((12•(b4))•(c-6))•———————————————)•(2•5b(-5)c)

(3•5b3c4)

STEP

52b(-1)c(-3)

Simplify ————————————

(3•5b3c4)

Dividing exponential expressions :

4.1 b(-1) divided by b3 = b((-1) - 3) = b(-4) = 1/b4

Dividing exponential expressions :

4.2 c(-3) divided by c4 = c((-3) - 4) = c(-7) = 1/c7

Dividing exponents:

4.3 52 divided by 51 = 5(2 - 1) = 51 = 5

Equation at the end of step

(((12•(b4))•(c-6))•—————)•(2•5b(-5)c)

3b4c7

STEP

Equation at the end of step

(((22•3b4) • c(-6)) • —————) • (2•5b(-5)c)

3b4c7

STEP

Canceling Out :

6.1 Canceling out b4 as it appears on both sides of the fraction line

Dividing exponential expressions :

6.2 c(-6) divided by c7 = c((-6) - 7) = c(-13) = 1/c13

Canceling Out:

6.3 Canceling out 3 as it appears on both sides of the fraction line

Equation at the end of step

——— • (2•5b(-5)c)

c13

STEP

Multiplying exponents:

7.1 22 multiplied by 21 = 2(2 + 1) = 23

Multiplying exponents:

7.2 51 multiplied by 51 = 5(1 + 1) = 52

Dividing exponential expressions :

7.3 c1 divided by c13 = c(1 - 13) = c(-12) = 1/c12

Final result :

200

—————

b5c12 Answer:

Step-by-step explanation:

5 0

3 years ago