How many solutions does this equation have? 2/3(x - 5) + 1/3 = 4x - 10/3x - 3 Choices: (A)none (B)one (C)two (D)infinitely many

Distribute and Simplify: Simplify the left side of the equation by distributing 2/3 and adding 1/3. 2/3(x - 5) + 1/3 = 2/3x - 10/3 + 1/3 = 2/3x - 9/3 = 2/3x - 3 Combine Like Terms: Simplify the right side of the equation by combining like terms. 4x - 10/3x - 3 = (12/3x - 10/3x) - 3 = 2/3x - 3 Set Equal: Set the simplified left side equal to the simplified right side. 2/3x - 3 = 2/3x - 3 Subtract and Simplify: Subtract 2/3x from both sides to see if the equation simplifies further. 2/3x - 3 - 2/3x = 2/3x - 3 - 2/3x 0 = 0

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Algebra 1

Find the number of solutions to a linear equation

Full solution

Q. How many solutions does this equation have?

\newline

\frac{2}{3}(x - 5) + \frac{1}{3} = 4x - \frac{10}{3}x - 3

\newline

Choices:

\newline

(A) none

\newline

(B) one

\newline

\newline

(D) infinitely many

Distribute and Simplify: Simplify the left side of the equation by distributing $\frac{2}{3}$ and adding $\frac{1}{3}$ . $\frac{2}{3}(x - 5) + \frac{1}{3} = \frac{2}{3}x - \frac{10}{3} + \frac{1}{3} = \frac{2}{3}x - \frac{9}{3} = \frac{2}{3}x - 3$
Combine Like Terms: Simplify the right side of the equation by combining like terms. $\newline$ $4x - \frac{10}{3}x - 3$ $\newline$ = $\left(\frac{12}{3}x - \frac{10}{3}x\right) - 3$ $\newline$ = $\frac{2}{3}x - 3$
Set Equal: Set the simplified left side equal to the simplified right side. $\frac{2}{3}x - 3 = \frac{2}{3}x - 3$
Subtract and Simplify: Subtract $\frac{2}{3}x$ from both sides to see if the equation simplifies further. $\newline$ $\frac{2}{3}x - 3 - \frac{2}{3}x = \frac{2}{3}x - 3 - \frac{2}{3}x$ $\newline$ $0 = 0$