Extra Practice 1
Lesson 6.1: Solving Equations1. Look at the algebraic expressions and equations below.
Which are expressions? Equations? How do you know?
a) 5x = 65 b) y + 8 c) 3a – 6
d) z + 3 = 9 e) f) 3q – 5 = 19
2. Solve by systematic trial.
a) d + 9 = 23 b) = 6
c) 3c – 5 = 16 d) 2x + 3 = 17
e) 4y = 52 f) 2e + 7 = 31
3. Solve by inspection.
a) 5a = 35 b) x + 7 = 13 c) p – 8 = 15
d) 2z – 3 = 13 e) 3d + 7 = 19 f) 4c – 1 = 19
4. Write an equation you could use to solve each problem.
Solve each equation by systematic trial.
a) Andrew lost 15 hockey cards. He has 37 left.
How many hockey cards did he have to start with?
b) Abba bought 15 DVD’s for $255. She paid the same amount for each DVD. How much did Abba pay for each DVD?
c) Stacy shared 35 candies equally among her group of friends. Each friend was given five candies. How many friends were in the group?
5. Write an equation for each sentence.
Solve each equation by inspection.
a) Six more than a number is 17.
b) Five less than a number is 23.
c) Three times a number is 18.
d) A number divided by four is 8.
e) Two more than three times a number is 17.
f) Five less than twice a number is 9.
6. Jason has 57 math puzzles. He keeps 9 for himself, then divides
the rest equally among his 8 friends.
a) Write an equation you can use to find the number of puzzles
given to each friend.
b) Solve the equation.
Extra Practice 2
1. a) Sketch balance scales to represent each equation.
b) Solve each equation.
Verify the solution.
i) x + 7 = 12 ii) z + 3 = 9
iii) 2y = 8 iv) 4a = 20
v) 2m + 1 = 13 vi) 2p + 3 = 27
vii) k + k + 7 = 19 viii) 5 + 3n = 20
2. a) Write an equation for each sentence.
b) Solve each equation.
Verify the solution.
i) Seven more than a number is 29.
ii) A number increased by nine is 23.
iii) Four times a number is 24.
iv) Three more than twice a number is 25.
v) Six more than three times a number is 27.
vi) A number multiplied by twelve is 84.
3. Suppose the masses for balance scales are only available in multiples of 6 g.
a) Sketch balance scales to represent the equation: 18 + x = 42
b) Solve the equation.
Verify the solution.
4. Suppose the masses for balance scales are only available in multiples of 8 g.
a) Sketch balance scales to represent the equation: 3x + 24 = 72
b) Solve the equation.
Verify the solution.
5. Use this equation: x + a = 15
a) What value of a will give the solution x = 9?
b) What value of a will give the solution x = 3?
Extra Practice 3
1. Use tiles to solve each equation. Sketch the tiles you used.
a) x + 5 = 11 b) 4 + x = 9 c) 13 = x + 8
d) x – 3 = 5 e) x – 7 = 3 f) 11 = x – 2
2. Solve by inspection. Show your work.
a) p – 7 = 9 b) q + 8 = 27 c) 3 = k – 6
d) s – 7 = –3 e) x + 3 = –4 f) x + 5 = 2
3. a) Six less than a number is 7.
Let x represent the number.
Write an equation you could use to find the value of x.
Solve the equation.
What is the number?
b) Three less than a number is –5.
Let x represent the number.
Write an equation you could use to find the value of x.
Solve the equation.
What is the number?
4. A group of 27 students visited an art exhibition.
Eleven of the students left after one hour.
The rest of the students stayed for a second hour.
How many students stayed for the second hour?
Write an equation you can use to find how many students stayed
for the second hour.
Solve the equation. Verify the solution.
5. Write an equation you can use to solve each problem below.
Solve each equation.
a) Overnight, the temperature dropped 6oC to –10oC.
What was the original temperature?
b) During the day, the temperature rose 7oC to +2oC.
What was the original temperature?
c) Overnight, the temperature dropped 8oC to –3oC.
What was the original temperature?
Extra Practice 4
1. Solve each equation using algebra. Verify each solution.
a) x – 29 = 13 b) 8x = 72 c) 7x = 49
d) x + 19 = 73 e) 3x – 8 = 46 f) 2x + 11 = 55
2. Write, then solve, an equation to find each number. Verify the solution.
a) Seventeen more than a number is 73.
b) Thirteen less than a number is 47.
c) A number multiplied by six is 54.
d) Seven more than three times a number is 31.
e) Five less than two times a number is 29.
f) Nine more than nine times a number is 99.
3. Write an equation you can use to solve each problem below.
Solve the equation. Verify the solution.
a) Sharon baby-sat on Saturday for $7/h. She was paid a bonus of $5.
How many hours did Sharon baby-sit if she was paid $40?
b) David worked in a store and was paid $8/h. He was paid a bonus of $9.
How many hours did David work if he was paid $65?
c) Sarah worked in a coffee shop at the weekend and was paid $6/h. She was given a bonus of $12. How many hours did Sarah work if she was paid $90?
4. Write an equation you can use to solve each problem below.
Solve the equation. Verify the solution.
a) Jeremy has $84 in his savings account. Each week he saves $18.
When will he have a total of $210?
b) Sandra has $172 in her savings account. Each week she saves $23.
When will she have a total of $264?
5. Write an equation you can use to solve each problem below.
Solve the equation. Verify the result.
a) At a tennis court, it costs $12 to rent equipment plus $6/h to rent a court.
How long can you play for $30?
b) At a fishing camp, it costs $15 to rent equipment plus $12/h to rent a boat. How long can you fish for $75?
c) At the skate park, it costs $8 to rent equipment plus $3/h to use the rink.
How long can you skate for $20?
Extra Practice 5
1. Use algebra to solve each equation. Verify each solution.
a) = 4 b) = 5 c) = 1
2. Solve each equation using the method of your choice.
a) x + 11 = 23 b) x – 9 = 17 c) 7x = 77
d) = 8 e) 2x + 13 = 31 f) 3x – 5 = 16
3. A banquet hall charged $120 for the rental of the hall, plus $14 for each
meal served. The total bill for the banquet was $610.
How many people attended the banquet?
Write, then solve, an equation to answer this question. Verify the solution.
4. Marshall baked 33 cookies. He kept five for himself, and shared the rest
equally among his friends. Each friend got 4 cookies.
Write, then solve, an equation you could use to find the number of friends
who got cookies.
5. Write, then solve, an equation to answer each question. Verify the solution.
Ms. Shapiro was organizing her class of 38 students into groups.
a) She divided the class into 8 equal groups and had 6 students left over.
How many students were in each group?
b) She divided the students into 5 equal groups and had 3 students left over.
How many students were in each group?
6. Write, then solve, an equation to answer each question. Verify each solution.
At Rose’s Garden Centre, a 5-kg bag of fertilizer costs $8 and
a 10-kg bag costs $14.
a) Rose sold $202 worth of fertilizer. She sold six 5-kg bags.
How many 10-kg bags did she sell?
b) Rose sold $206 worth of fertilizer. She sold five 10-kg bags.
How many 5-kg bags did she sell?
7. Write, then solve, an equation to answer each question. Verify each solution.
a) One more than three times a number is 28. What is the number?
b) Four less than five times a number is 31. What is the number?
c) Twice a number increased by seven is 29. What is the number?
d) Seventeen added to three times a number is 53. What is the number?
Extra Practice Sample Answers
Extra Practice 1 – Master 6.18
Lesson 6.1
1. Expressions: b, c, e
I know they are expressions because they do not have an equals sign.
Equations: a, d, f
I know they are equations because they each contain an equals sign.
2. a) d = 14 b) p = 24 c) c = 7
d) x = 7 e) y = 13 f) e = 12
3. a) a = 7 b) x = 6 c) p = 23
d) z = 8 e) d = 4 f) c = 5
4. a) x – 15 = 37; x = 52; he had 52 cards to start with.
b) 15n = 255; n = 17; she paid $17 for each DVD.
c) 5n = 35; n = 7; there were 7 friends in the group.
5. a) n + 6 = 17; n = 11; the number is eleven.
b) n – 5 = 23; n = 28; the number is twenty-eight.
c) 3n = 18; n = 6; the number is six.
d) = 8; n = 32; the number is thirty-two.
e) 3n + 2 = 17; n = 5; the number is five.
f) 2n – 5 = 9; n = 7; the number is seven.
6. a) 57 – 9 = 8n, or 48 = 8n
b) n = 6; each friend was given 6 puzzles.
Extra Practice 2 – Master 6.19
Lesson 6.2
1. a) Students’ solutions should include sketches.
b) i) x = 5; L.S. = x + 7 = 5 + 7 = 12
R.S. = 12
ii) z = 6; L.S. = z + 3 = 6 + 3 = 9
R.S. = 9
iii) y = 4; L.S. = 2y = 2 × 4 = 8
R.S. = 8
iv) a = 5; L.S. = 4a = 4 × 5 = 20
R.S. = 20
v) m = 6; L.S. = 2m + 1 = 2 × 6 + 1 = 13
R.S. = 13
vi) p = 12; L.S. = 2p + 3 = 2 × 12 + 3 = 27
R.S. = 27
vii) k = 6; L.S. = k + k + 7 = 6 + 6 + 7 = 19
R.S. = 19
viii) n = 5; L.S. = 5 + 3n = 5 + 3 × 5 = 20
R.S. = 20
2. i) a) n + 7 = 29 b) n = 22; the number is twenty-two.
ii) a) n + 9 = 23 b) n = 14; the number is fourteen.
iii) a) 4n = 24 b) n = 6; the number is six.
iv) a) 2n + 3 = 25 b) n = 11; the number is eleven.
v) a) 3n + 6 = 27 b) n = 7; the number is seven.
vi) a) 12n = 84 b) n = 7; the number is seven.
3. a) Left pan: x, 6 g, 12 g Right pan: 12 g, 6 g, 24 g
b) Remove 6 g and 12 g from each pan. Mass x balances with 24 g, so x = 24.
4. a) Left pan: x, x, x, 8 g, 16 g Right pan: 16 g, 32 g, 8 g, 16 g
b) Remove 8 g and 16 g from each pan. 3 identical unknown masses balance 32 g + 16 g = 48 g.
Replace 48 g with 16 g + 16 g + 16 g. Each unknown mass balances 16 g, so x = 16.
5. a) 9 + a = 15; a = 6
b) 3 + a = 15; a = 12
Extra Practice 3 – Master 6.20
Lesson 6.3
1. Students’ solutions should include sketches.
a) x = 6 b) x = 5 c) x = 5
d) x = 8 e) x = 10 f) x = 13
2. a) p = 16 b) q = 19 c) k = 9
d) s = 4 e) x = –7 f) x = –3
3. a) x – 6 = 7; x = 13; the number is thirteen.
b) x – 3 = –5; x = –2; the number is –2.
4. 11 + n = 27; n = 16; sixteen students stayed for the second hour.
5. a) t – 6 = –10; t = –4; the original temperature was –4oC.
b) t + 7 = 2; t = –5; the original temperature was –5oC.
c) t – 8 = –3; t = 5; the original temperature was 5oC.
Extra Practice 4 – Master 6.21
Lesson 6.4
1. a) x = 42 b) x = 9 c) x = 7
d) x = 54 e) x = 18 f) x = 22
2. a) n + 17 = 73; n = 56; the number is fifty-six.
b) n – 13 = 47; n = 60; the number is sixty.
c) 6n = 54; n = 9; the number is nine.
d) 3n + 7 = 31; n = 8; the number is eight.
e) 2n – 5 = 29; n = 17; the number is seventeen.
f) 9n + 9 = 99; n = 10; the number is ten.
3. a) 7n + 5 = 40; n = 5; Sharon baby-sat for 5 h.
b) 8n + 9 = 65; n = 7; David worked for 7 h.
c) 6n + 12 = 90; n = 13; Sarah worked for 13 h.
4. a) 84 + 18n = 210; n = 7; Jeremy will have a total of $210 after 7 weeks.
b) 172 + 23n = 264; n = 4; Sandra will have a total of $264 after 4 weeks.
5. a) 12 + 6h = 30; h = 3; you can play for 3 h.
b) 15 + 12h = 75; h = 5; you can fish for 5 h.
c) 8 + 3h = 20; h = 4; you can skate for 4 h.
Extra Practice 5 – Master 6.22
Lesson 6.5
1. a) x = 28 b) x = 25 c) x = 12
2. a) x = 12 b) x = 26 c) x = 11
d) x = 40 e) x = 9 f) x = 7
3. 120 + 14n = 610; n = 35; 35 people attended the banquet.
4. 33 – 5 = 4n, or 28 = 4n; n = 7; seven friends got cookies.
5. a) 8n + 6 = 38; n = 4; there were 4 students in each group.
b) 5n + 3 = 38; n = 7; there were 7 students in each group.
6. a) 6 × 8 + 14n = 202, or 48 + 14n = 202; n = 11; she sold eleven 10-kg bags.
b) 5 ×14 + 8n = 206, or 70 + 8n = 206; n = 17; she sold seventeen 5-kg bags.