Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for x and write your answer in simplest form. -(5)/(2)(-(1)/(2)x-4)+x=-(9x+(5)/(2))-1 Answer: x=

Solve for x x and write your answer in simplest form.\newline−52(−12x−4)+x=−(9x+52)−1 -\frac{5}{2}\left(-\frac{1}{2} x-4\right)+x=-\left(9 x+\frac{5}{2}\right)-1 \newlineAnswer: x= x=

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Multiplication with rational exponentsright chevron icon

Full solution

Q. Solve for x x and write your answer in simplest form.\newline−52(−12x−4)+x=−(9x+52)−1 -\frac{5}{2}\left(-\frac{1}{2} x-4\right)+x=-\left(9 x+\frac{5}{2}\right)-1 \newlineAnswer: x= x=
  1. Write Equation: Write down the given equation.\newlineThe given equation is: \newline−52(−12x−4)+x=−(9x+52)−1-\frac{5}{2}\left(-\frac{1}{2}x-4\right)+x=-\left(9x+\frac{5}{2}\right)-1
  2. Distribute Negative Sign: Distribute the negative sign on the left side of the equation.\newlineWe have to distribute the negative sign through the fraction on the left side:\newline−52×(−12x)+(−52×−4)+x-\frac{5}{2} \times \left(-\frac{1}{2}x\right) + \left(-\frac{5}{2} \times -4\right) + x\newlineThis simplifies to:\newline54x+10+x\frac{5}{4}x + 10 + x
  3. Combine Like Terms: Combine like terms on the left side.\newlineCombine (54)x(\frac{5}{4})x and xx (which is the same as (44)x(\frac{4}{4})x):\newline(54)x+(44)x+10(\frac{5}{4})x + (\frac{4}{4})x + 10\newlineThis simplifies to:\newline(94)x+10(\frac{9}{4})x + 10
  4. Distribute Negative Sign: Distribute the negative sign on the right side of the equation.\newlineWe have to distribute the negative sign through the parentheses on the right side:\newline−9x−(52)−1-9x - \left(\frac{5}{2}\right) - 1\newlineThis simplifies to:\newline−9x−(52)−(22)-9x - \left(\frac{5}{2}\right) - \left(\frac{2}{2}\right)
  5. Combine Constants: Combine the constants on the right side.\newlineCombine −52-\frac{5}{2} and −22-\frac{2}{2}:\newline−9x−72-9x - \frac{7}{2}
  6. Set Equal: Set the simplified left side equal to the simplified right side.\newline(94)x+10=−9x−(72)(\frac{9}{4})x + 10 = -9x - (\frac{7}{2})
  7. Move Terms: Move all terms involving xx to one side and constants to the other side.\newlineAdd 9x9x to both sides and subtract 1010 from both sides:\newline(94)x+9x=−(72)−10(\frac{9}{4})x + 9x = - (\frac{7}{2}) - 10
  8. Combine Like Terms: Combine like terms.\newlineConvert 9x9x to a fraction with the same denominator as (94)x(\frac{9}{4})x:\newline(94)x+(364)x=−(72)−10(\frac{9}{4})x + (\frac{36}{4})x = - (\frac{7}{2}) - 10\newlineThis simplifies to:\newline(454)x=−(72)−10(\frac{45}{4})x = - (\frac{7}{2}) - 10
  9. Convert 1010 to Fraction: Convert 1010 to a fraction with a denominator of 22 to combine with −(72)-\left(\frac{7}{2}\right). 1010 is the same as (202)\left(\frac{20}{2}\right): (454)x=−(72)−(202)\left(\frac{45}{4}\right)x = -\left(\frac{7}{2}\right) - \left(\frac{20}{2}\right)
  10. Combine Constants: Combine the constants on the right side.\newline- (72)−(202)(\frac{7}{2}) - (\frac{20}{2}) simplifies to:\newline- (272)(\frac{27}{2})\newlineSo we have:\newline(454)x=−(272)(\frac{45}{4})x = - (\frac{27}{2})
  11. Solve for x: Solve for x by dividing both sides by (45/4)(45/4).\newlineTo isolate xx, we divide both sides by (45/4)(45/4), which is the same as multiplying by the reciprocal, (4/45)(4/45):\newlinex=−(272)×(445)x = - \left(\frac{27}{2}\right) \times \left(\frac{4}{45}\right)
  12. Simplify Right Side: Simplify the right side.\newlineMultiply the numerators and the denominators:\newlinex=−27×42×45x = - \frac{27 \times 4}{2 \times 45}\newlinex=−10890x = - \frac{108}{90}
  13. Simplify Fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1818. \newlinex=−10818/9018x = - \frac{108}{18} / \frac{90}{18}\newlinex=−65x = - \frac{6}{5}

More problems from Multiplication with rational exponents

Question
Simplify.\newline811281^{\frac{1}{2}}\newline_____________
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify.\newline(−32)1/5(-32)^{1/5}\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify. Assume all variables are positive.\newlinew43w73\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify. Assume all variables are positive.\newline(2r13)8(2r^{\frac{1}{3}})^8\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify. Assume all variables are positive.\newlinev74⋅v94v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______\newline
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify.\newline114⋅1141^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify. \newline32(−1/5)32^{(-1/5)}
Get tutor helpright-arrow

Posted 7 months ago

Question
Simplify. Assume all variables are positive.\newlinew32w52\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______\newline
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify. Assume all variables are positive.\newline(27x)23(27x)^{\frac{2}{3}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
Get tutor helpright-arrow

Posted 8 months ago

Question
Simplify. Assume all variables are positive.\newlinex14x114\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______\newline
Get tutor helpright-arrow

Posted 7 months ago

View all (744)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant