Questions: Solve the equation for all values of x . 5x+9=4x

Solve the equation for all values of x . 5x+9=4x
Transcript text: Solve the equation for all values of x . \[ |5 x+9|=4 x \]
failed

Solution

failed
failed

To solve the equation \(|5x + 9| = 4x\), we need to consider two cases due to the absolute value: one where the expression inside the absolute value is non-negative, and one where it is negative. This will give us two separate linear equations to solve for \(x\).

  1. Case 1: \(5x + 9 \geq 0\), which simplifies to \(5x + 9 = 4x\).
  2. Case 2: \(5x + 9 < 0\), which simplifies to \(-(5x + 9) = 4x\).

Solve each equation separately and check the solutions against the conditions for each case.

Paso 1: Resolver el primer caso

Para el primer caso, donde \(5x + 9 = 4x\), simplificamos la ecuación:

\[ 5x + 9 = 4x \]

Restando \(4x\) de ambos lados, obtenemos:

\[ 5x - 4x + 9 = 0 \implies x + 9 = 0 \implies x = -9 \]

Paso 2: Verificar la condición del primer caso

Verificamos si \(x = -9\) satisface la condición \(5x + 9 \geq 0\):

\[ 5(-9) + 9 = -45 + 9 = -36 < 0 \]

Por lo tanto, \(x = -9\) no es una solución válida.

Paso 3: Resolver el segundo caso

Para el segundo caso, donde \(-(5x + 9) = 4x\), simplificamos la ecuación:

\[ -5x - 9 = 4x \]

Sumando \(5x\) a ambos lados, obtenemos:

\[ -9 = 4x + 5x \implies -9 = 9x \implies x = -1 \]

Paso 4: Verificar la condición del segundo caso

Verificamos si \(x = -1\) satisface la condición \(5x + 9 < 0\):

\[ 5(-1) + 9 = -5 + 9 = 4 \geq 0 \]

Por lo tanto, \(x = -1\) no es una solución válida.

Resumen de soluciones

No encontramos soluciones válidas para la ecuación \(|5x + 9| = 4x\).

Respuesta Final

\(\boxed{\text{No hay solución}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Assume that all grade-point averages are to be standardized on a scale b of the population mean? Assume that a 95% confidence level is desired. seem practical? The required sample size is □ (Round up to the nearest whole number as needed.)
failedAnswered
Skills Required Knowledge of principles of employee selection and assignment Ability to express ideas clearly both orally and in writing Ability to independently plan and organize one's own activities Knowledge of human resources computer applications desirable Duties Prepares recruitment literature and job advertisements for applicant placement Reviews résumés to identify qualified applicants Conducts interviews to determine applicant's suitability for employment
failedAnswered
Fill in each blank so that the resulting statement is true. Consider the line whose equation is 7x + y - 6 = 0. The slope of any line that is parallel to this line is . The slope of any line that is perpendicular to this line is . The slope of any line that is parallel to this line is (Type an integer or a simplified fraction.)
failedAnswered
uestion 6 of 11 Which response would the nurse provide when asked by a pregnant patient with newly diagnosed varicose veins how to prevent more from developing? "Be sure to rest often in a sitting position." "The varicose veins will disappear after you have given birth." "Wear graduated compression stockings and frequently elevate your legs." "These will have to be removed during a surgical procedure to prevent further spread." NOT SURE CONFIDENT Search
failedAnswered
Which of the following statements about summarizing key ideas in a speech conclusion are true? - It helps listeners retain the information. - The summary should be brief. - Listeners lose interest if key ideas are summarized in the conclusion. - It grabs the audience's attention.