Question

PLEASE HELP PLEASEEEEE
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 5−x and y = 2x + 1 intersect are the solutions of the equation 5−x = 2x + 1.
Part B: Make tables to find the solution to 5−x = 2x + 1. Take the integer values of x between −3 and 3.
Part C: How can you solve the equation 5−x = 2x + 1 grap hically?​

Answer 1

Part A

We know these points are the solutions to $5-x=2x+1$ because by setting the two equations equal to each other, we find where they intersect, and those points are the solutions to the equation.

Part B

$\boxed {\begin{array}{c|c|c|c}\cline{1-4}\bf x&\bf5-x&\bf2x+1&\bf5-x=2x+1\\\cline{1-4}-3&8&-5&8\neq-5\\\cline{1-4}-2&7&-3&7\neq-3\\\cline{1-4}-1&6&-1&6\neq-1\\\cline{1-4}0&5&1&0\neq1\\\cline{1-4}1&4&3&4\neq3\\\cline{1-4}2&3&5&3\neq5\\\cline{1-4}3&2&7&2\neq7\\\cline{1-4}\end{array}}$

Part B and a half

Since none of those values are correct solutions, let's solve this equation algebraically, even though the question doesn't ask for us to do so.

$\begin{aligned}5-x&=2x+1\\-x&=2x+1-5\\-x-2x&=1-5\\-3x&=-4\\x&=\boxed{\frac{4}{3}}\end{aligned}$

Part C

We can solve the equation graphically by graphing both $y=5-x$ and $y=2x+1$, then finding where they meet. This is shown in the attachment below.

Answer 2

Hope it helps you ♡♡♡♡♡♡♡