Question

(2x + 1) - (4x + 3)Subtracting BinomialsCan you graph the binomials? After you subtract the equation. (2x + 1) - (4x + 3)

Answer 1

We have the following operation with two binomials:

`(2x+1)-(4x+3)`

And we have to find the result of the subtraction, and then graph that result.

To find the result of the subtraction, we can proceed as follows:

1. Multiply the second binomial by -1:

`\begin{gathered} (2x+1)-4x-3 \\ \\ 2x+1-4x-3 \end{gathered}`

2. Add - algebraically - the like terms:

`\begin{gathered} 2x-4x+1-3 \\ \\ -2x-2 \end{gathered}`

Therefore, the result for the subtraction is -2x - 2:

`(2x+1)-(4x+3)=-2x-2`

3. Now, to graph the result of the binomial, we can see that we have a line in the slope-intercept form:

`\begin{gathered} y=mx+b \\ \\ y=-2x-2 \end{gathered}`

And we know that b is the y-intercept of the line, that is, the line passes through the point (0, -2). The y-intercept is a point where the line passes through the y-axis when x = 0. We also can see that the slope of the line is negative, m = -2.

4. We can find the x-intercept so that we can graph the line easily using the intercepts. We know that the x-intercept is the point where the line passes through the x-axis when y = 0. Then we have to set it to zero y in the resulting equation above:

`\begin{gathered} y=-2x-2\rightarrow y=0 \\ \\ 0=-2x-2 \\ \\ 2x=-2 \\ \\ (2x)/(2)=-(2)/(2) \\ \\ x=-1 \\ \end{gathered}`

Therefore, the x-intercept is (-1, 0).

5. Now we can graph the resulting line by using the two resulting points: (-1, 0) and (0,-2). Then we have:

Therefore, in summary, we have that:

• The result of subtracting both binomials is ,-2x - 2

,

• And the graph of this result is (a line):