Given the equation 2x+1 =3, solve for x amd identify if its an extraneous solution.

x=1, and x is not extraneous

Step-by-step explanation:

First you must solve for x. By using inverse operations, you must isolate x. When using inverse operations, you should do the addition and subtraction first, so you subtract 1 from both sides. This leaves you with 2x=2. 3 has become 2 because you subtracted 1 from it, and because you have to subtract 1 from both sides. Now you need to divide both sides by 2. This leaves you with x=1. To determine whether or not this is extraneous, we must plug x=1 back into the equation. This leaves us with 2(1)+1=3. By using the order of operations, we multiply first and then add. We first multiply 2 and 1, giving us 2. We have 2+1=3. We now add 2+1, giving us 3. Since 3=3, x is not extraneous.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be