Algebra 1 - Chapter 1 Review

Solving Equations

100

4(x+3) - 2x = 16

x = 2

200

3x - (x+7) = -9

x = -1

300

2x + 6 = 5x - 15

x = 7

400

2(x-5) - 4(x-2) = 3 - 3x

x = 5

500

4x + 7 = 8(x-1) + 1

x = 7/2 or 3 1/2 or 3.5

Number of Solutions:0, 1, or Infinity

100

3x + 7 = 2x + (x + 6)

7=6 => NO SOLUTION

200

6x + 8 = 4(x+2)

x = 0 => ONE SOLUTION

300

3x - (8-2x) = -8 + 5x

-8 = -8 => INFINITELY MANY SOLUTIONS

400

3(2x+6) = 2(2x-7) + 24

x = -4 => ONE SOLUTION

500

4(x+7) - 3(2-x) = 5(x+3) + 2(5+x)

22 = 25 => NO SOLUTION

Absolute Value Equations

100

| x+8| = 2

x = -6 OR x = -10 (NEED BOTH)

200

| 2x+1 | = 3

x = 1 OR x = -2 (NEED BOTH)

300

| 4x+5 | = -10

Absolute Value cannot equal a negative => NO SOLUTION

400

| x-5 | - 3 = -2

x = 6 OR x = 4 (NEED BOTH)

500

3 | 2x+3 | + 7 = 13

x = -1/2 OR x = -5/2 (NEED BOTH)

Literal Equations

100

Solve for x. y = 3x + 1

x = ( y-1 ) / 3

200

Solve for h. V = lwh

h = V / (lw)

300

Solve for w. 6P = 12d + 2w

w = 3P - 6d

400

Solve for x. y = 3x + xz

x = y / (3+z)

500

Solve for y. 5x + y = 2 - xy

y = (2-5x) / (1+x)

Word Problems

100

WRITE AN EQUATION & SOLVE: Rob drives for 2 1/2 hours, traveling 160 miles total. What is his average speed?

x - Rob's average speed. ~ d = rt ~ 160 = x (2.5) ~ x = 64 ~ Rob's average speed is 64 MPH.

200

WRITE AN EQUATION & SOLVE: Sally buys t-shirts for her Relay for Life team. She has to pay $5 for a setup fee and then pays $8 per shirt. How many shirts did she order if it costs $93?

x - number of shirts ~ 5 + 8x = 93 ~ x = 11 ~ Sally buys 11 shirts.

300

WRITE AN EQUATION & SOLVE: Three consecutive even integers have a sum of 18. Find the integers.

x - First Even Integer ~ x+2 - Next Even Integer ~ x+4 - Third Even Integer ~ x + (x+2) + (x+4) = 18 ~ x = 4 ~ The three integers are 4, 6, and 8.

400

WRITE AN EQUATION & SOLVE: Find four consecutive integers such that the sum of the first two is 15 less than triple the largest.

x - first integer ~ x+1 - second integer ~ x+2 - third integer ~ x+3 - fourth integer ~ x + (x+1) = 3(x+3) - 15 ~ x = 7 ~ The integers are 7, 8, 9, and 10.

500

WRITE AN EQUATION & SOLVE: The width of a rectangle is 1/2 of it length. Its perimeter is 21 inches. Find its dimensions.

x - length ~ 1/2 x - width ~ x + 1/2 x + x + 1/2 x = 21 ~ x = 7 ~ The rectangle is 7 inches x 3.5 inches.