UNIT 1: Equivalent Trick and Solving Trick

Which is equivalent to 4(x + 3)?

A. 4x+3

B. 4x+12

C. x+12

B. 4x + 12 (Distribute 4: 4·x + 4·3.)

Which is equivalent to 5(x − 2)?

A. 5x−2

B. 5x+10

C. 5x−10

D. x−10

C. 5x − 10 (Distribute 5 to both terms.)

Which is equivalent to 7x + 2x − 5?

A. 9x−5

B. 9x+5

C. 5x−5

A. 9x − 5 (Combine 7x + 2x.)

Simplify: 3(x + 4) − 2x

A. x+12

B. 5x+12

C. x+4

A. x + 12 (3x + 12 − 2x = x + 12.)

Which is equivalent to 2(x + 5) + 3x?

A. 5x+5

B. 5x+10

C. 6x+10

B. 5x + 10 (2x + 10 + 3x = 5x + 10.)

Which is equivalent to 6x − 18?

A. 6(x−3)

B. 6(x−18)

C. 3(x−6)

A. 6(x − 3) (Factor out the common factor 6.)

Which is equivalent to 3x + 12?

A. 3(x+4)

B. 3(x+12)

C. x+4

A. 3(x + 4) (Factor out 3.)

Which is equivalent to 2(x − 3) + 4(x + 1)?

A. 6x−2

B. 6x+2

C. 8x−2

A. 6x − 2 (2x−6 + 4x+4 = 6x−2.)

Simplify: 3(x + 2) − 2(x − 1)

A. x+4

B. x+8

C. 5x+8

B. x + 8 (3x+6−2x+2 = x+8.)

Which is equivalent to 4(x − 2) + 3x?

A. 7x−8

B. 7x−2

C. x−8

A. 7x − 8 (4x−8 + 3x = 7x−8.)

Solve: 3x + 5 = 20

A. x=3

B. x=5

C. x=7

B. x = 5 (3x = 15, so divide by 3.)

Solve: 4x − 6 = 10

A. x=2

B. x=3

C. x=4

C. x = 4 (4x = 16, then divide by 4.)

Solve: 2(x + 3) = 14

A. x=4

B. x=5

C. x=7

D. x=11

A. x = 4 (x + 3 = 7, so x = 4.)

Solve: 5x + 2 = 3x + 12

A. x=4

B. x=5

C. x=6

D. x=10

B. x = 5 (2x = 10, so x = 5.)

Which Desmos method finds the solution to 2x + 6 = 14?

A. Graph both sides and find the intersection

B. Use the y-intercept

C. Use the slope

A. Graph both sides and find the intersection (The x-coordinate is the solution.)

Solve for y: x + y = 9

A. y=x+9

B. y=−x+9

C. y=x−9

B. y = −x + 9 (Subtract x from both sides.)

Solve for y: 2x + y = 10

A. y=2x+10

B. y=−2x+10

C. y=2x−10

D. y=−2x−10

B. y = −2x + 10 (Subtract 2x from both sides.)

Solve for y: 2x + 3y = 12

A. y=−2/3x+4

B. y=−2x+4

C. y=2/3x+4

A. y = −2/3x + 4 (Subtract 2x, then divide by 3.)

How can Desmos check if two expressions are equivalent?

A. Compare their graphs

B. Compare slopes only

C. Add them

A. Compare their graphs (Equivalent expressions produce the same graph.)

How can Desmos check your y = answer?

A. Graph both equations

B. Find only the slope

C. Add the coefficients

A. Graph both equations (If they produce the same line, your form is equivalent.)