Algebra Workshop
Name:
Worksheet 3
1. Solve the following equations.
√
3x + 1 + 7 = 4
(a) 3 − 2x2 = −5
(b)
(c) 3x2 + 5 = x2 + 13
(d) (x + 2)2 − 4 = 5
(e) 5 − | x| = 3
(f) | x + 4| − 3 = 2
2. Simplify the following expressions:
(a) 5x2 + 3y − 2x2 + 4y 2 − 2y
(b) 5(3x2 − 5y) − 2x2 + 4x
(c) 3x(y − x) + 2x2 + 5xy + 3y
3. Solve for a in the following equation:
5(2a + b) − 3(a + 3b) = 5
4. Solve for y in the following equation:
x2 + y 2 = 36
2
5. Find the prime factorizations of the following numbers:
(a) 18
(b) 45
(c) 24
(d) 210
6. Evaluate:
(a)
1
1
+
2
4
(b) 1 −
(c)
1
− 1
3
(d)
3
1
−
2
4
(e)
1
2
+
3
7
(f)
1
1
+
8
4
3
1
2
7. Evaluate:
(a)
2 10
1 6
·
− ·
5 3
3 5
(b)
1
5
÷
3
9
(c)
2/5
3/8
(d)
1/3
5
8. Evaluate:
(a)
3
1
1
−
2
4
2
6
−
7
(b) 5
8
4
9. Solve the following problems. Give your answers to 2 decimal places.
(a) What is 41% of 30?
(b) What percent of 30 is 15?
(c) 20 is 40% of what?
(d) What is 150% of 300?
10. Sales tax in New York City is 8.875%.
(a) If the listed price of an item is $10.99, what is the sales tax?
(b) If the listed price of an item is $5.49, how much do you pay for the item (including
the sales tax)?
5
11. A voter registration campaign in a particular city increases the number of registered voters
by 25%. If there were 6000 voters before the campaign, how many are there afterwards?
12. A store is having a 30% sale on all of it shirts. (In the following problems, assume that
there is no sales tax.)
(a) If a shirt was previously being sold for $20, how much does it cost now?
(b) Zach buys a shirt from the store; he pays $17.50 for the shirt. How much would the
shirt have cost before the sale? (Be careful with this problem. Let x be the original
cost of the shirt. Set up an equation involving x and then solve.)
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