Juanita wants to model the equation 3 x + 2 = negative x + 6. She begins with the tiles below. 3 x tiles and 2 positive 1 tiles = 1 negative x tile How can Juanita complete her model? Put 4 yellow unit tiles on the left side of the equal sign. Put 4 yellow unit tiles on the right side of the equal sign. Put 6 green x-tiles on the right side of the equal sign. Put 6 yellow unit tiles on the right side of the equal sign.

Step-by-step explanation:

Given the equation that Juanita wants to model expressed by the equation

3 x + 2 = -x + 6

If she begins with 3 x tiles and 2 positive 1 tiles = 1 negative x tile, she will b=need to complete her model with put 6 yellow unit tiles on the right side of the equal sign since the only value left at the right hand side of the equation is positive 6

We can as well calculate the value of x from the expression as shown;

3 x + 2 = -x + 6

collect like terms

3x+x = 6-2

4x = 4

Divide both sides by 4

4x/4 = 4/4

x = 1

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4