Question

directions: solve each equation and color the object that corresponds with your answer. show your steps!!!

1. $2(x + 1) = 3x - 1$

(a) if your answer is $x = 3$ color the chin strap attached to the helmet black.
(b) if your answer is $x = 2$ color the chin strap attached to the helmet green.

1. $3n + 1 = -n + 2$

(a) if your answer is $n = -\frac{1}{4}$ color the helmet shades of yellow and brown.
(b) if your answer is $n = \frac{1}{4}$ color the helmet shades of green and brown.

1. $-2(x + 1) = 3x + 1$

(a) if your answer is $x = \frac{3}{5}$ color the ears, nose, face, neck and arms brown.
(b) if your answer is $x = -\frac{3}{5}$ color the ears, nose, face, neck and arms apricot.

1. $2(x + 1) + 2 = 3x - 4$

(a) if your answer is $x = 8$ color the eyes blue.
(b) if your answer is $x = 7$ color the eyes green.

1. $-3(2x - 3) = -5x + 5$

(a) if your answer is $x = -14$ outline the eyes and eyebrows in orange.
(b) if your answer is $x = 4$ outline the eyes and eyebrows in black.

1. $\frac{1}{3}(6x + 9) = x - 5$

(a) if your answer is $x = -8$ outline the nose in black.
(b) if your answer is $x = -14$ outline the nose in orange.

1. $5(n + 2) - 8 = 2n$

(a) if your answer is $n = -\frac{2}{3}$ color the shapes under the eyes black.
(b) if your answer is $n = 2$ color the shapes under the eyes brown.

1. $-3x = 4(3x - 2) + 1$

(a) if your answer is $x = \frac{7}{15}$ outline the mouth in red.
(b) if your answer is $x = \frac{8}{15}$ outline the mouth in black.

1. $2(x + 1) = -3(x - 2)$

(a) if your answer is $x = -\frac{8}{5}$ color the straps on the backpack green.
(b) if your answer is $x = \frac{4}{5}$ color the straps on the backpack black.

1. $3(2m - 3) = 5(m + 1)$

(a) if your answer is $m = 14$ color the backpack brown.
(b) if your answer is $m = 10$ color the backpack green.

1. $-4(3m + 5) = -2(m - 2)$

(a) if your answer is $m = \frac{12}{5}$ color the shirt collar brown.
(b) if your answer is $m = -\frac{12}{5}$ color the shirt collar green.

1. $3(n + 1) - 2 = 4(2n + 3)$

(a) if your answer is $n = -\frac{9}{5}$ color the shirt shades of yellow and brown.
(b) if your answer is $n = -\frac{11}{5}$ color the shirt shades of green and brown.

1. $2(x + 5) - 3 = -(2x + 1) + 1$

(a) if your answer is $x = -\frac{5}{4}$ outline the scar in red.
(b) if your answer is $x = -\frac{7}{4}$ outline the scar in black.

1. $2(m + 1) = 3m$

(a) if your answer is $m = 2$ color the stripes on the american flag red and white.
(b) if your answer is $m = -2$ color the stripes on the american flag pink and white.

1. $-(x + 1) = 2x$

(a) if your answer is $x = \frac{1}{3}$ color the background of the section with stars on the american flag purple.
(b) if your answer is $x = -\frac{1}{3}$ color the background of the section with stars on the american flag blue.
artistic tip: when you are done coloring, it looks nice to outline the major...

Explanation:

Step1: Solve equation 13: \(2(x + 1)=3x - 1\)

Expand left side: \(2x+2 = 3x - 1\)
Subtract \(2x\) from both sides: \(2=x - 1\)
Add 1 to both sides: \(x = 3\)

Step2: Solve equation 14: \(3n + 1=-n + 2\)

Add \(n\) to both sides: \(4n+1 = 2\)
Subtract 1: \(4n = 1\)
Divide by 4: \(n=\frac{1}{4}\)

Step3: Solve equation 15: \(-2(x + 1)=3x + 1\)

Expand left: \(-2x-2 = 3x + 1\)
Add \(2x\) to both sides: \(-2 = 5x+1\)
Subtract 1: \(-3 = 5x\)
Divide by 5: \(x=-\frac{3}{5}\)

Step4: Solve equation 16: \(2(x + 1)+2 = 3x - 4\)

Expand: \(2x+2 + 2=3x - 4\)
Simplify: \(2x + 4=3x - 4\)
Subtract \(2x\): \(4=x - 4\)
Add 4: \(x = 8\)

Step5: Solve equation 17: \(-3(2x - 3)=-5x + 5\)

Expand: \(-6x + 9=-5x + 5\)
Add \(6x\) to both sides: \(9=x + 5\)
Subtract 5: \(x = 4\)

Step6: Solve equation 18: \(\frac{1}{3}(6x + 9)=x - 5\)

Simplify left: \(2x+3 = x - 5\)
Subtract \(x\): \(x+3=-5\)
Subtract 3: \(x=-8\)

Step7: Solve equation 19: \(5(n + 2)-8 = 2n\)

Expand: \(5n+10 - 8=2n\)
Simplify: \(5n + 2=2n\)
Subtract \(5n\): \(2=-3n\)
Divide by -3: \(n=-\frac{2}{3}\)

Step8: Solve equation 20: \(-3x = 4(3x - 2)+1\)

Expand right: \(-3x=12x - 8 + 1\)
Simplify: \(-3x=12x - 7\)
Subtract \(12x\): \(-15x=-7\)
Divide by -15: \(x=\frac{7}{15}\)

Step9: Solve equation 21: \(2(x + 1)=-3(x - 2)\)

Expand: \(2x+2=-3x + 6\)
Add \(3x\): \(5x+2 = 6\)
Subtract 2: \(5x = 4\)
Divide by 5: \(x=\frac{4}{5}\)

Step10: Solve equation 22: \(3(2m - 3)=5(m + 1)\)

Expand: \(6m-9 = 5m + 5\)
Subtract \(5m\): \(m-9 = 5\)
Add 9: \(m = 14\)

Step11: Solve equation 23: \(-4(3m + 5)=-2(m - 2)\)

Expand: \(-12m-20=-2m + 4\)
Add \(12m\): \(-20 = 10m+4\)
Subtract 4: \(-24 = 10m\)
Divide by 10: \(m=-\frac{12}{5}\)

Step12: Solve equation 24: \(3(n + 1)-2 = 4(2n + 3)\)

Expand: \(3n+3 - 2=8n + 12\)
Simplify: \(3n + 1=8n + 12\)
Subtract \(3n\): \(1 = 5n+12\)
Subtract 12: \(-11 = 5n\)
Divide by 5: \(n=-\frac{11}{5}\)

Step13: Solve equation 25: \(2(x + 5)-3=-(2x + 1)+1\)

Expand: \(2x+10 - 3=-2x - 1+1\)
Simplify: \(2x + 7=-2x\)
Add \(2x\): \(4x+7 = 0\)
Subtract 7: \(4x=-7\)
Divide by 4: \(x=-\frac{7}{4}\)

Step14: Solve equation 26: \(2(m + 1)=3m\)

Expand: \(2m+2 = 3m\)
Subtract \(2m\): \(2 = m\)

Step15: Solve equation 27: \(-(x + 1)=2x\)

Expand: \(-x - 1=2x\)
Add \(x\): \(-1 = 3x\)
Divide by 3: \(x=-\frac{1}{3}\)

(Note: Since the problem asks to solve each equation and color the corresponding object, the above steps show the solution for each equation. For example, for equation 13, \(x = 3\), so we color the chin strap attached to the helmet black as per option (a) of equation 13. Similar logic applies to other equations.)

Answer:

Step1: Solve equation 13: \(2(x + 1)=3x - 1\)

Expand left side: \(2x+2 = 3x - 1\)
Subtract \(2x\) from both sides: \(2=x - 1\)
Add 1 to both sides: \(x = 3\)

Step2: Solve equation 14: \(3n + 1=-n + 2\)

Add \(n\) to both sides: \(4n+1 = 2\)
Subtract 1: \(4n = 1\)
Divide by 4: \(n=\frac{1}{4}\)

Step3: Solve equation 15: \(-2(x + 1)=3x + 1\)

Expand left: \(-2x-2 = 3x + 1\)
Add \(2x\) to both sides: \(-2 = 5x+1\)
Subtract 1: \(-3 = 5x\)
Divide by 5: \(x=-\frac{3}{5}\)

Step4: Solve equation 16: \(2(x + 1)+2 = 3x - 4\)

Expand: \(2x+2 + 2=3x - 4\)
Simplify: \(2x + 4=3x - 4\)
Subtract \(2x\): \(4=x - 4\)
Add 4: \(x = 8\)

Step5: Solve equation 17: \(-3(2x - 3)=-5x + 5\)

Expand: \(-6x + 9=-5x + 5\)
Add \(6x\) to both sides: \(9=x + 5\)
Subtract 5: \(x = 4\)

Step6: Solve equation 18: \(\frac{1}{3}(6x + 9)=x - 5\)

Simplify left: \(2x+3 = x - 5\)
Subtract \(x\): \(x+3=-5\)
Subtract 3: \(x=-8\)

Step7: Solve equation 19: \(5(n + 2)-8 = 2n\)

Expand: \(5n+10 - 8=2n\)
Simplify: \(5n + 2=2n\)
Subtract \(5n\): \(2=-3n\)
Divide by -3: \(n=-\frac{2}{3}\)

Step8: Solve equation 20: \(-3x = 4(3x - 2)+1\)

Expand right: \(-3x=12x - 8 + 1\)
Simplify: \(-3x=12x - 7\)
Subtract \(12x\): \(-15x=-7\)
Divide by -15: \(x=\frac{7}{15}\)

Step9: Solve equation 21: \(2(x + 1)=-3(x - 2)\)

Expand: \(2x+2=-3x + 6\)
Add \(3x\): \(5x+2 = 6\)
Subtract 2: \(5x = 4\)
Divide by 5: \(x=\frac{4}{5}\)

Step10: Solve equation 22: \(3(2m - 3)=5(m + 1)\)

Expand: \(6m-9 = 5m + 5\)
Subtract \(5m\): \(m-9 = 5\)
Add 9: \(m = 14\)

Step11: Solve equation 23: \(-4(3m + 5)=-2(m - 2)\)

Expand: \(-12m-20=-2m + 4\)
Add \(12m\): \(-20 = 10m+4\)
Subtract 4: \(-24 = 10m\)
Divide by 10: \(m=-\frac{12}{5}\)

Step12: Solve equation 24: \(3(n + 1)-2 = 4(2n + 3)\)

Expand: \(3n+3 - 2=8n + 12\)
Simplify: \(3n + 1=8n + 12\)
Subtract \(3n\): \(1 = 5n+12\)
Subtract 12: \(-11 = 5n\)
Divide by 5: \(n=-\frac{11}{5}\)

Step13: Solve equation 25: \(2(x + 5)-3=-(2x + 1)+1\)

Expand: \(2x+10 - 3=-2x - 1+1\)
Simplify: \(2x + 7=-2x\)
Add \(2x\): \(4x+7 = 0\)
Subtract 7: \(4x=-7\)
Divide by 4: \(x=-\frac{7}{4}\)

Step14: Solve equation 26: \(2(m + 1)=3m\)

Expand: \(2m+2 = 3m\)
Subtract \(2m\): \(2 = m\)

Step15: Solve equation 27: \(-(x + 1)=2x\)

Expand: \(-x - 1=2x\)
Add \(x\): \(-1 = 3x\)
Divide by 3: \(x=-\frac{1}{3}\)

(Note: Since the problem asks to solve each equation and color the corresponding object, the above steps show the solution for each equation. For example, for equation 13, \(x = 3\), so we color the chin strap attached to the helmet black as per option (a) of equation 13. Similar logic applies to other equations.)