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Home > AC > Chapter 10 > Lesson 10.1.2 > Problem 10-22

10-22.

Solve the equations below. Check your solution(s).

$\frac { m } { 6 } = \frac { m + 1 } { 5 }$
Hint (a):
Multiply by the least common denominator to factor out the denominators.
More Help (a):
The LCM of $6$ and $5$ is $30$ .

$5m=6\left(m+1\right)$
Answer (a):
$m=-6$

$\frac { 3 x - 5 } { 2 } = \frac { 4 x + 1 } { 4 }$
Hint (b):
Refer to part (a).

$\frac { 8 } { k } = \frac { 14 } { k + 3 }$
Hint (c):
Multiply by the least common denominator. In this case, the LCD is $k\left(k+3\right)$ .
More Help (c):
$8\left(k+3\right)=14k$

$\frac { x } { 9 } = 10$
Hint (d):
Any whole number can be rewritten so it has a denominator of $1$ . So,
$10 = \frac{10}{1}$
More Help (d):
Refer to part (a).

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