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:

How many solutions does this equation have?\newline23(x−5)+13=4x−103x−3\frac{2}{3}(x - 5) + \frac{1}{3} = 4x - \frac{10}{3}x - 3\newlineChoices:\newline(A) none\newline(B) one\newline(C) two\newline(D) infinitely many

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Find the number of solutions to a linear equationright chevron icon

Full solution

Q. How many solutions does this equation have?\newline23(x−5)+13=4x−103x−3\frac{2}{3}(x - 5) + \frac{1}{3} = 4x - \frac{10}{3}x - 3\newlineChoices:\newline(A) none\newline(B) one\newline(C) two\newline(D) infinitely many
  1. Distribute and Simplify: Simplify the left side of the equation by distributing 23\frac{2}{3} and adding 13\frac{1}{3}.23(x−5)+13=23x−103+13=23x−93=23x−3\frac{2}{3}(x - 5) + \frac{1}{3} = \frac{2}{3}x - \frac{10}{3} + \frac{1}{3} = \frac{2}{3}x - \frac{9}{3} = \frac{2}{3}x - 3
  2. Combine Like Terms: Simplify the right side of the equation by combining like terms. \newline4x−103x−34x - \frac{10}{3}x - 3 \newline= (123x−103x)−3\left(\frac{12}{3}x - \frac{10}{3}x\right) - 3 \newline= 23x−3\frac{2}{3}x - 3
  3. Set Equal: Set the simplified left side equal to the simplified right side. 23x−3=23x−3\frac{2}{3}x - 3 = \frac{2}{3}x - 3
  4. Subtract and Simplify: Subtract 23x\frac{2}{3}x from both sides to see if the equation simplifies further.\newline23x−3−23x=23x−3−23x\frac{2}{3}x - 3 - \frac{2}{3}x = \frac{2}{3}x - 3 - \frac{2}{3}x\newline0=00 = 0

More problems from Find the number of solutions to a linear equation

Question
Solve for x. \newline(34)x=12(\frac{3}{4})x= 12 \newlinex=x = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve for x. \newline−59x=15-\frac{5}{9}x= 15 \newlinex=x = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
How many solutions does the following equation have?\newline5x+8−7x=−4x+15x+8-7x=-4x+1\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline−2z+10+7z=16z+7-2z+10+7z=16z+7\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline7(y−8)=7y+427(y-8)=7y+42\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline−9(x+6)=−9x+108-9(x+6)=-9x+108\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline−6(x+7)=−4x−2-6(x+7)=-4x-2\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline−4x−7+10x=−7+6x-4x-7+10x=-7+6x\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline−17(y−2)=−17y+64-17(y-2)=-17y+64\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

Question
How many solutions does the following equation have?\newline9z−6+7z=16z−69z-6+7z=16z-6\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 4 months ago

View all (192)