One-Step Equations
n+7=31
n=24
-15=-4m+5
m=5
Write and solve an equation for the following word problem: Liam had some marbles and gave 4 away. He has 9 marbles left. How many marbles did he have originally?
x-4=9
13 marbles
Write and solve an equation for the following word problem: Ava buys 3 identical notebooks and pays an additional $2 for a pencil. Her total is $17. How much does each notebook cost?
3x+2=17
$5
This letter or symbol represents an unknown number in an equation, such as x+5=12.
Variable
6=(a/2)
a=12
28-8x=92
x=-8
Write and solve an equation for the following word problem: A student read some pages on Monday and 18 more pages on Tuesday. The student read 30 pages altogether. How many pages did she read on Monday?
x+18=30
12 pages
Write and solve an equation for the following word problem: A number is divided by 3, and then 4 is added. The result is 10. What is the number
(x/3)+4=10
18 is the number
These are operations that undo each other, such as addition and subtraction or multiplication and division.
Inverse Operations
-4=(r/20)
r=-80
10-6v=-104
v=19
Write and solve an equation for the following word problem: A savings account increased by $24. The account now has $61. How much money was in the account before the increase?
x+24=61
$37
Write and solve an equation for the following word problem: A taxi ride costs a $6 starting fee plus $3 per mile. If the total fare is $30, how many miles was the ride?
3x+6=30
8 miles
This means replacing a variable with a number to see if your solution makes the equation true.
Substitute
(3/4)g=-3
g=-4
-1=(5+x)/6
Write and solve an equation for the following word problem: Movie tickets cost $8 each. A group spent $56 on tickets. How many tickets did the group buy?
8x=56
7 tickets
Write and solve an equation for the following word problem: A baker divides some cookies equally among 5 trays. After removing 2 cookies from each tray, each tray has 10 cookies. How many cookies did the baker originally put on each tray?
(x/5) - 2 = 10
12 cookies per tray
This is a number that, when multiplied by a nonzero number, gives a product of 1. For example, 4/3 is this number for 3/4.
Reciprocal
-15v=-90
v=6
(n+15)/-16=-1
n=1
Write and solve an equation for the following word problem: A school divides students equally into 12 groups. Each group has 28 students. How many students are there altogether?
(x/12)=28
336 students
Write and solve an equation for the following word problem: A warehouse packs the same number of items into each of 8 boxes. After 16 items are removed from the total, 120 items remain. How many items were originally packed in each box?
8x - 16 = 120
17 items
This means getting the variable alone on one side of an equation.
Isolate