Mathematics, 02.03.2020 06:44 benallyadam2067

When you solve the equation x + 1 = 2x for x, the solution is 1. 1) Square both sides of the equation, and verify that your solution satisfies the new equation. 2) Show that −1/3 satisfies the new equation but not the original equation.

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Answer from: abdirahmansoloman

Part 1: The solution of the new equation is x=1 and $x=-\frac{1}{3}$ and the two solutions satisfies the new equation.

Part 2: The solution $x=-\frac{1}{3}$ satisfies the new equation but not the original equation.

Explanation:

Part 1: The given equation is x+1=2 x

We need to square both sides of the equation and verify that the solution satisfies the new equation.

Now, squaring both sides of the equation, we get,

(x+1)^2=(2 x)^2

Thus, the new equation is (x+1)^2=(2 x)^2

Let us solve the new equation to determine the solution.

$x^{2} +2x+1=4x^{2}$

$4x^{2}-x^{2} -2x-1=0$

$3x^{2} -2x-1=0$

Taking factors, we get,

3x(x-1)+1(x-1)=0

(3x+1)(x-1)=0

$x=-\frac{1}{3} ,1$

Thus, the solution of the new equation is x=1 and $x=-\frac{1}{3}$

Now, we shall verify the solution x=1 and $x=-\frac{1}{3}$ that satisfies the new equation (x+1)^2=(2 x)^2

Substituting x=1 in (x+1)^2=(2 x)^2 , we get,

(1+1)^2=(2 (1))^2

(2)^2=(2)^2

4=4

Since, both sides of the equation are equal, the solution x=1 satisfies the new equation.

Also, substituting $x=-\frac{1}{3}$ in (x+1)^2=(2 x)^2 , we get,

$(-\frac{1}{3} +1)^2=(2 (-\frac{1}{3} ))^2$

$(\frac{2}{3} )^2=(-\frac{2}{3} )^2$

$\frac{4}{9} =\frac{4}{9}$

Since, both sides of the equation are equal, the solution $x=-\frac{1}{3}$ satisfies the new equation.

Thus, the solutions x=1 and $x=-\frac{1}{3}$ satisfies the new equation.

Part 2: Now, we need to show that the solution $x=-\frac{1}{3}$ satisfies the new equation but not the original equation.

Substituting $x=-\frac{1}{3}$ in the new equation, we get,

(x+1)^2=(2 x)^2

$(-\frac{1}{3} +1)^2=(2 (-\frac{1}{3} ))^2$

$(\frac{2}{3} )^2=(-\frac{2}{3} )^2$

$\frac{4}{9} =\frac{4}{9}$

Since, both sides of the equation are equal, the solution $x=-\frac{1}{3}$ satisfies the new equation.

Now, substituting $x=-\frac{1}{3}$ in the original equation, we have,

x+1=2 x

$-\frac{1}{3} +1=2 (-\frac{1}{3} )$

$\frac{2}{3} =-\frac{2}{3}$

Since, both sides of the equation are not equal, the solution $x=-\frac{1}{3}$ does not satisfies the original equation.

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

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 = $\frac{1-0}{3-0} = \frac{1}{3}$ .

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

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

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

$y> \frac{1}{3}x$ .

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

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

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

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

5050 i think

step-by-step explanation:

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When you solve the equation x + 1 = 2x for x, the solution is 1. 1) Square both sides of the equatio...