Quarter 1 Algebra Review 2024

Literal Equations

100

4abc = d   Solve for b

d / (4ac)

200

5a - b = c,  solve for a

(c + b) / 5

300

12a + 3b = 5a + 2, solve for a

(2 - 3b) / 7

400

a/b = c/d, solve for b

ad / c

500

g = 6 (h + 4), solve for h

h = (g-24)/6   or g/6 - 4

Add/Sub Polynomials

100

Find the sum

(a + 5) + (a + 6)

2a + 11

200

Simplify

(5a² + 4a - 3)+(3a² - 2a + 6)

8a² + 2a + 3

300

Find the difference of 2(3x³ + 4x) and 5x² - x

6x³ - 5x² + 9x

400

Find the difference

(9v² - 4v) - (2v² + 5v)

7v² - 9v

500

Simplify

3(4m² + 7) -  2(5m² - 8)

2m² + 37

Variables on Both Sides

100

7x + 12 = -4x + 78

x = 6

200

3(3m - 2) = 2(3m + 3)

m = 4

300

6(3a + 1) - 30 = 3(2a - 4)

a = 1

400

3.2k - 4.3 = 12.6k + 14.5

k = -2

500

1/3(5x + 3) = 1/2x + 4

x = 2  4/7

Inequalities

100

-1/2x > 5

x < -10

200

3x - 5 > 40

x > 15

300

-3/5x + 7 < 22

x > -25

400

5𝑥 + 2(𝑥 + 1) ≥ 23

x ≥ 3

500

4(3 − 𝑥) − 3(4 − 𝑥) > −15

x<15

Story Problems

100

On Monday, a restaurant made $545 from selling 110 hamburgers.  If they sold 53 on Tuesday, how much did they make?  

They made $262.59

200

The Toyota Prius drove 208 miles on 5 gallons of gas.  How far should it be able to go on a full, 11 gallon tank?

457.6 miles

300

Two thirds of a number reduced by 11 is equal to 4 more than the number.  Find the number.  

The number is - 45

400

Ben has $56 saved and works for $14 per hour at Culvers.  If he wants to make more than $300 to buy a gaming system, how many hour (h) would he need to work?  Write an inequality to represent this situation.   

14h + 56 > 300

500

Write an equation where the Coefficients are the same and the constants are different.  What does this mean for the equation?

This means that there is no solution that will make the equation true.