Solving One-Variable Equations

CLT & DP

100

3x + 5x

8x

200

8x - 2 + -7x

x - 2

300

3(x - 4) + 2 - 14x

-11x - 10

400

-(x-1) + 3(x-4)

2x - 11

500

-3(x - 4) - (6x + 2)

-9x + 2

Multi-step Equations

100

2p + 1 = 21

p = 10

200

7p - 9 = -30

p = -3

300

2(x + 1) = 18

x = 8

400

6(t - 3) = -60

t = -7

500

5y + 5(y - 3) = -63

y = -24/5 or -4.8

Variables on Both Sides

100

2x = x + 5

x = 5

200

x + 1 = 3x - 5

x = 3

300

2(3c - 8) = -8c - 2

c = 1

400

-2(-7a + 4) = 5(a - 16)

a = -8

500

-3(d - 1) = d/5 + 3

d = 0

Grab Bag!

100

Absolute value means...

The distance a number is from zero.

200

3x - 7 = 3x + 4

What kind of solution is this?

No solution!

300

Define like terms.

Terms with the same variable AND the same exponent on the same side of the equal sign.

**constants (numbers without variables) are also like terms.

400

3(x + 2) - 1 = 3x + 7 + (-2)

Infinite solutions

500

What is the population of Minneapolis?

*within 5,000

425,000 (circa 2020)

Absolute Value Equations

100

[x] = 7

x = 7, -7

200

[x - 3] = 4

x = -1, 7

300

[2x - 3] + 5 = 12

x = -2, 5

400

2[2x - 5] - 9 = -1

x = 1/2, 9/2

500

1/2[x-2] = -2

NO SOLUTIONS! 

We cannot have [x-2] = -4. Absolute value cannot equal a negative number!