Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for all values of
x in simplest form.

10+|2x+5|=22
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $10+|2 x+5|=22$ $\newline$ Answer: $x=$

View step-by-step help

View step-by-step help

Solve logarithmic equations with multiple logarithms

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

10+|2 x+5|=22

\newline

Answer:

x=

Isolate absolute value: Write down the equation and isolate the absolute value expression. $\newline$ We have the equation $10 + |2x + 5| = 22$ . To isolate the absolute value, we subtract $10$ from both sides of the equation. $\newline$ $10 + |2x + 5| - 10 = 22 - 10$ $\newline$ $|2x + 5| = 12$
Set up equations: Set up two separate equations to account for the absolute value. $\newline$ Since the absolute value of a number can be either positive or negative, we have two cases: $\newline$ $2x + 5 = 12$ or $2x + 5 = -12$
Solve positive case: Solve the first equation where the inside of the absolute value is positive. $\newline$ $2x + 5 = 12$ $\newline$ Subtract $5$ from both sides: $\newline$ $2x = 12 - 5$ $\newline$ $2x = 7$ $\newline$ Divide both sides by $2$ : $\newline$ $x = \frac{7}{2}$ $\newline$ $x = 3.5$
Solve negative case: Solve the second equation where the inside of the absolute value is negative. $\newline$ $2x + 5 = -12$ $\newline$ Subtract $5$ from both sides: $\newline$ $2x = -12 - 5$ $\newline$ $2x = -17$ $\newline$ Divide both sides by $2$ : $\newline$ $x = \frac{-17}{2}$ $\newline$ $x = -8.5$

More problems from Solve logarithmic equations with multiple logarithms

Question

Solve. Write your answer as an integer or a fraction in simplest form.

\newline

5^x=1

\newline

x=

Posted 2 months ago

Question

Steven opened a savings account and deposited

\$100.00

as principal. The account earns

9\%

interest, compounded annually. What is the balance after

5

\newline

Use the formula

A = P(1 + \frac{r}{n})^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years.

\newline

Round your answer to the nearest cent.

\newline

\$

Posted 2 months ago

Question

Use the following function rule to find

f(1)

\newline

f(x) = 12(7)^x + 8

\newline

f(1) =

Posted 1 month ago

Question

The town of Valley View conducted a census this year, which showed that it has a population of

1,800

people. Based on the census data, it is estimated that the population of Valley View will grow by

12\%

\newline

Write an exponential equation in the form

y = a(b)^x

that can model the town population,

y

x

decades after this census was taken.

\newline

Use whole numbers, decimals, or simplified fractions for the values of

a

b

\newline

y =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = 9^x

\newline

x =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 1 month ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 2 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 1 month ago

Question

g(t) = 3^t

change over the interval from

t = 3

t = 4

\newline

\newline

g(t)

3

\newline

g(t)

3

\newline

g(t)

3\%

\newline

g(t)

200\%

Posted 2 months ago

Question

f(x)

6

over every unit interval in

x

f(0) = 0

\newline

Which could be a function rule for

f(x)

\newline

\newline

f(x) = 6^x

\newline

f(x) = 6x

\newline

f(x) = \frac{1}{6^x}

\newline

f(x) = \frac{x}{6}

Posted 2 months ago