Math 7
Lesson: Solving Two-Step Equations
And Word Problems
Name_____________________________
Block________ Date_________________
REVIEW STEPS FOR SOLVING TWO-STEP EQUATIONS:
1. Separate equation sides with a
down through the = sign, and
2. Label the variable side of the equation.
3. On the variable side, circle the term that does not have a variable with it.
4. Cancel out that term you circled, by doing its inverse operation (“undo” or “cancel out”).
Remember to do that inverse operation on BOTH sides of the equation!
5. If the variable term is being multiplied by a number, then divide both sides of the
equation by that number, and you are finished solving.
If the variable term is being divided by a number, then multiply both sides of the
equation by that number, and you are finished solving.
REVIEW PRACTICE:
a) 3x  17  13
d)
2
x  11  15
7
g) 25  2x  1
b)
5
x   20
7
e) 31  x  14
h)
2
x  11  15
7
c)  x  5   12
f)
3
x  6   18
4
i) 19  x   7
4.4 Two-step word problems
1. CONSTRUCTION Nick is building a screen
door. The height of the door is 1 ft more than
twice its width. What is the width of the door if
it is 7 feet high?
Let w =
Name: __________________
2. GEOMETRY A rectangle has a width of 6
inches and a perimeter of 26 inches. What is
the length of the rectangle?
Let L =
3. HOME IMPROVEMENT Patty is making a
patio in her backyard using paving stones.
She buys 44 paving stones and a flowerpot
worth $7 for a total of $73. How much did
each paving stone cost?
4. SHOPPING While at the music store, Jack
bought 5 CDs, all at the same price. The tax on
his purchase was $6, and the total was $61.
What was the price of each CD?
5. TAXI A taxi service charges you $1.50 plus
$0.60 per minute for a trip to the airport. The
distance to the airport is 10 miles, and the total
charge is $13.50. How many minutes did the
ride to the airport take?
6. FOOD At the market, Drew buys a bunch of
bananas for $0.35 per pound and a frozen
pizza for $4.99. The total for his purchase was
$6.04, without tax. How many pounds of
bananas did Drew buy?
7. SHARING Aliyah had some candy to share.
She first took ten pieces for herself and then
evenly divided the rest among her four cousins.
Each cousin received two pieces. With how
many pieces did she start?
8. AGE How old am I if 400 reduced by 2 times
my age is 244?
9. BUY AND SELL Jill sold half of her comic
books and then bought sixteen more. She now
has 36. With how many did she begin?
10. TRANSPORTATION For a field trip, 4
students can ride in cars and the rest must
be divided evenly to ride in nine buses. How
many students were in each bus if 472
students were on the trip?
11. HATS On Tuesday Andres bought five
12. FUNDRAISING The SHMS Orchestra was
selling donuts as a fundraiser. Billy Jean sold
fourteen dozen donuts for $70. How much
did each dozen cost? How many donuts
total did she sell?
baseball caps. On Wednesday he gave
half of all his hats away as gifts to
friends. On Thursday there were only 17
left. How many did he have on Monday?
Write and solve an equation for each problem.
HOMEWORK 4.4
1. Eleven less than 5 times a number is 24. Find the number.
2.
The quotient of a number and -9, increased by 10, is 11. Find the number.
3.
Three more than 8 times a number is -29. Find the number.
4. The Nile River is 6690 kilometers long. This is 394 kilometers longer than the Amazon River.
How long is the Amazon River?
5.
The Empire State Building is 1250 feet tall. This is 140 feet more than twice the height of the
Washington Monument. How tall is the Washington Monument?
6.
A medium apple has 72 calories. This is ¾ of the calories in a medium banana. How many calories
does a medium banana have?
7.
The width of a singles tennis court is 27 feet. This is 1 foot more than 3 of the length. What is the
length of the court?
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