Algebra 1 Topic 1 Review

Solving Simple Equations

100

w-1/5=2/5

w=3/5

200

-3b=9

b=-3

300

-8q=24

q=-4

400

The difference of 3 times a number and 5 is 13. Write and solve an equation to find the number.

3x-5=13

x=6

500

The measure of the larger angle of an isosceles triangle is four times the measure of each of the other two angles. Find the measure of the larger angle.

120 degrees

s+s+4s=180

4s=120

Multi-Step Equations

100

2(x+2)-7=7

x=5

200

6y-8-6-8y=4

y=-9

300

-7(x+7)=-56

x=1

400

4(4m-3)-(m-5)=-52

m=-3

500

You order two coffees and a cookie. The cookie costs $2.40. You pay 5% sales tax and leave a $1.75 tip. You pay a total of $11.20. How much does one coffee cost?

$346

Variables on Both Sides

100

Two shops each charge a rental fee plus an hourly fee to rent a canoe. How many hours must a canoe be rented for the total costs at both shops to be the same?

Shop A: Rental: $2 Hourly: $5

Shop B: Rental: $8 Hourly: $4

6 hours

200

7-6v=-5-8v

v=-6

300

-4(x+5)=5(x-4)

No solution

400

5(x+6)-2x=3(x+10)

infinitely many solutions

500

4/3=8/(x-1)

x=7

Absolute Value

100

abs(2x+6)+1=3

x={-2,-4}

200

The recommended mass m of a baseball is 145 grams. The actual mass is allowed to vary by up to 2 grams. What are the minimum and maximum allowed baseball masses?

minimum=143

maximum=147

300

abs(3b+9)-16=5

b={4, -10}

400

Consider the equation

abs(1/6x-3)=x/3

. Without calculating, is x=-6 a solution?

No

500

-10abs(h+5)-3=-83

h={3, 13}

Rewriting Equations

100

V=lwh

Solve for h

h=V/(lw)

200

Solve the literal equation

5y+8x=-5

 for y.

y=(-8x-5)/5

300

p=2L+2W

W=(P-2L)/2

400

The volume of a cone is given by the formula

V=1/3pir^2h

, where r is the radius of the base and h is the height. Solve the formula for h.

h=(3V)/(pir^2)

500

The letters a and b represent nonzero constants. Solve  ax-b=30 for x.

x=(b+30)/a