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?\newline89x−13x+4=59(x+2)\frac{8}{9}x - \frac{1}{3}x + 4 = \frac{5}{9}(x + 2)\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?\newline89x−13x+4=59(x+2)\frac{8}{9}x - \frac{1}{3}x + 4 = \frac{5}{9}(x + 2)\newlineChoices:\newline(A) none\newline(B) one\newline(C) two\newline(D) infinitely many
  1. Combine like terms: Combine like terms on the left side of the equation.\newline89x−13x\frac{8}{9}x - \frac{1}{3}x can be simplified by finding a common denominator, which is 99.\newline89x−39x=59x\frac{8}{9}x - \frac{3}{9}x = \frac{5}{9}x.\newlineSo, the equation becomes 59x+4=59(x+2)\frac{5}{9}x + 4 = \frac{5}{9}(x + 2).
  2. Distribute on right side: Distribute 59\frac{5}{9} on the right side of the equation.\newline59(x+2)=59x+109\frac{5}{9}(x + 2) = \frac{5}{9}x + \frac{10}{9}.\newlineNow, the equation is 59x+4=59x+109\frac{5}{9}x + 4 = \frac{5}{9}x + \frac{10}{9}.
  3. Subtract to isolate constants: Subtract 59x\frac{5}{9}x from both sides to isolate the constants.\newline59x+4−59x=59x+109−59x\frac{5}{9}x + 4 - \frac{5}{9}x = \frac{5}{9}x + \frac{10}{9} - \frac{5}{9}x.\newlineThis simplifies to 4=1094 = \frac{10}{9}.

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)