Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$-4 + bx = 2x + 3(x + 1)$ In the equation shown, $b$ is a constant. For what value of $b$ does the equation have no solutions?

View step-by-step help

View step-by-step help

Write a linear equation from a slope and y-intercept

Full solution

Q.

-4 + bx = 2x + 3(x + 1)

In the equation shown,

b

is a constant. For what value of

b

does the equation have no solutions?

Identify Structure and Condition: Identify the structure of the given equation and the condition for no solutions. $\newline$ The equation is in the form of a linear equation, and for it to have no solutions, the coefficients of $x$ on both sides must be equal, and the constants must be different. This is because if the lines represented by both sides of the equation have the same slope but different $y$ -intercepts, they are parallel and will never intersect.
Expand and Simplify: Expand the right side of the equation to simplify it. $\newline$ $2x + 3(x + 1) = 2x + 3x + 3$ $\newline$ Combine like terms. $\newline$ $2x + 3x + 3 = 5x + 3$
Combine Like Terms: Set up the equation to compare the coefficients of $x$ on both sides. $\newline$ For the equation to have no solutions, the coefficient of $x$ on the left side (which is $b$ ) must be equal to the coefficient of $x$ on the right side (which is $5$ ). $\newline$ So, $b$ must be equal to $5$ .
Set Up Equation for Coefficients: Check if the constants on both sides are different when $b$ is $5$ . On the left side, the constant is $-4$ , and on the right side, the constant is $3$ . Since $-4$ is not equal to $3$ , the condition for no solutions is satisfied when $b = 5$ .

More problems from Write a linear equation from a slope and y-intercept

Question

(0, 4)

satisfy the equation

y = x

?

\newline

Choices: [[yes]][[no]]

Posted 2 months ago

Question

Find the slope of the line

y = -4x + \frac{2}{5}

\newline

Write your answer as an integer or as a simplified proper or improper fraction.

Posted 1 month ago

Question

Rewrite the following equation in slope-intercept form.

\newline

y + 8 = -8(x - 10)

\newline

Write your answer using integers, proper fractions, and improper fractions in simplest form.

\newline

Posted 1 month ago

Question

y

-intercept of the line

14x - 16y = -10

\newline

Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

\newline

Posted 1 month ago

Question

q

\frac{-2}{3}

r

is perpendicular to

q

. What is the slope of line

r

\newline

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

\newline

\_\_\_\_\_

Posted 1 month ago

Question

Find the slope of the line

y + 3 = -\frac{1}{18}(x + 6)

\newline

Write your answer as an integer or as a simplified proper or improper fraction.

Posted 1 month ago

Question

p

has an equation of

y = -8x + 6

q

, which is perpendicular to line

p

, includes the point

(2, -2)

. What is the equation of line

q

?

\newline

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

\newline

Posted 1 month ago

Question

Is the graph of this equation a horizontal or vertical line?

\newline

x = 7

\newline

\newline

\text{(A)horizontal line}

\newline

\text{(B)vertical line}

Posted 2 months ago

Question

Rewrite the following equation in standard form.

\newline

y = -10x + 7

\newline

Hint: The standard form of a linear equation is

\newline

Ax + By = C

A

B

are not both zero, and

A

B

C

are integers whose GCF is

1

Posted 2 months ago

Question

A line with a slope of

9

passes through the point

(9,9)

. What is its equation in point-slope form?

\newline

Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

\newline

y - \underline{\hspace{1cm}} = \underline{\hspace{1cm}} (x - \underline{\hspace{1cm}})

Posted 1 month ago