Algebra Workshop
Name:
Worksheet 1
1. Evaluate the following expressions:
(a) 3 − 2 · 5 + 4
(b) 3 · 7 − 2 · 32 − 5
(c) (2)(−6) − 3(4 − 5 · 3)
(d) 2(4 − 7)2
(e) 4 · 23 − 5
(f)
8 + 4·5
2·7
2. Suppose I choose a number. I multiply this number by 3; then I add 10. The result is 46.
(a) Write an equation that describes this situation.
(b) Solve the equation to find the original number.
3. Suppose I choose a number. I add 4 to this number; then I multiply by 3. The result is
15.
(a) Write an equation that describes this situation.
(b) Solve the equation to find the original number.
4. For each of the following equations, write a description of what the equation means (similar
to the descriptions in problems 2 and 3). In addition, you should solve the equation.
(a)
x
−5 = 7
2
(b)
x+3
= 7
4
2
5. Solve the following equations:
(a) 3x − 4 = 5
(b) 5x + 1 = 7
(c) 3(x + 2) = 9
(d) 4(x + 1) = 8
(e)
3x
= 9
7
(f)
x
−4 = 6
2
(g)
3x − 5
= 4
4
(h)
x+3
−2 = 3
5
3
6. Solve the following equations:
(a) 10 = 4 + 2x
(b) 23 − x = 9
(c) x − 3 = 7x
(d) 2(x − 1) = 5x + 4
(e) 3(x − 2) + 4(x + 1) = 12
(f) 2(3x − 5) − 3(x − 2) = 5
4
7. Simplify the following expressions:
(a) x + 5y − 3x − 2y
(b) 5(3y − 2) − (7y + 2)
(c) 7(x + 2y) − 2(3x − 5y)
8. Solve for y in the following equations:
(a) 6x + 2y = 4
(b) 12x + 9y = 6y − 9
5
9. Josh has a bag of apples. He eats half of the apples, and then he buys 8 more apples.
Afterwards, there are 12 apples in the bag.
(a) Let x be the initial number of apples in the bag. Write an equation that describes
the situation.
(b) Solve the equation.
10. A mother has some pieces of candy to split among her children. She first takes 3 pieces
of candy for herself, and then she evenly divides the rest among her 4 children. If each
child receives 6 pieces of candy, how many pieces of candy did the mother have to start
with?
(a) Write the equation that describes this situation.
(b) Solve the equation.
6
11. Becky is five years older than Jimmy. The sum of their ages is 19.
(a) Let x be Jimmy’s age. Write an equation to determine Jimmy’s age.
(b) Solve the equation. How old are Becky and Jimmy?
12. A middle school has 196 students in grades 6th, 7th, and 8th. There are twice as many
7th graders as 6th graders, and there are 20 more 8th graders than 6th graders. How
many students are there in 6th, 7th, and 8th grade?
7