Simple equations in one variable

Advanced Math 7 · Unit 5 · linear-equations-7 · Teacher edition

linear-equations-7

Name ______________________________Date ______________

1.
Solve $5x - 7 = 3x + 9$ .
Answer: ______________
2.
Solve $\dfrac{x + 5}{3} = \dfrac{x - 1}{2}$ .
Answer: ______________
3.
Maya is three times as old as Ben. In $8$ years she will be twice as old as Ben will be then. How old is Ben now?
Answer: ______________
4.
Solve $\dfrac{x}{3} + 2 = \dfrac{x}{4} + 5$ .
1. (A)
  $3$
2. (B)
  $12$
3. (C)
  $36$
4. (D)
  $84$
5.
The length of a rectangle is $3$ cm more than twice its width. Its perimeter is $48$ cm. What is its area, in cm²?
1. (A)
  $63$
2. (B)
  $105$
3. (C)
  $119$
4. (D)
  $144$
5. (E)
  $238$

Answer key — Simple equations in one variable

1.
8linear-equations-7-01
$5x - 7 = 3x + 9 \Rightarrow 2x = 16 \Rightarrow x = \mathbf{8}$ . Check: $40 - 7 = 33$ and $24 + 9 = 33$ . ✓
2.
13linear-equations-7-02
$6 \times \frac{x + 5}{3} = 2(x + 5)$ and $6 \times \frac{x - 1}{2} = 3(x - 1)$ , so $2x + 10 = 3x - 3$ and $x = \mathbf{13}$ . Check: $\frac{18}{3} = 6 = \frac{12}{2}$ . ✓
3.
8linear-equations-7-03
$3b + 8 = 2b + 16 \Rightarrow b = \mathbf{8}$ . Ben is $8$ and Maya is $24$ ; in $8$ years they are $16$ and $32$ , and $32 = 2 \times 16$ . ✓
4.
(C)
$36$
linear-equations-7-04
$12\left(\frac{x}{3} + 2\right) = 4x + 24$ and $12\left(\frac{x}{4} + 5\right) = 3x + 60$ , so $x = \mathbf{36}$ . Check: $12 + 2 = 14$ and $9 + 5 = 14$ . ✓ ( $3$ comes from $4x + 2 = 3x + 5$ , forgetting to multiply the constants; $84$ adds $60 + 24$ instead of subtracting.)
5.
(C)
$119$
linear-equations-7-05
$2(3w + 3) = 48 \Rightarrow 3w + 3 = 24 \Rightarrow w = 7$ . Length $= 2(7) + 3 = 17$ . Area $= 7 \times 17 = \mathbf{119}$ cm². ( $238 = 14 \times 17$ uses $2w$ as the width; $144 = 12^2$ treats the rectangle as a square with perimeter $48$ .)