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10-69.

Solve the equations below, if possible. If there is no solution, explain why.

$\frac { 8 - x } { x } = \frac { 3 } { 2 }$
Step 1 (a):
Multiply both sides by $2x$ .
$2x\left(\frac{8-x}{x}\right)=\left(\frac{3}{2}\right)2x$
Step 2 (a):
Distribute the $2$ to both terms and simplify the right side.
$8(2)-x(2)=3x$
Step 3 (a):
Combine like terms on one side.
$16=5x$
Answer (a):
$x=\frac{16}{5}$

$- 2 ( 5 x - 1 ) - 3 = - 10 x$
Hint (b):
Distribute the $-2$ and then simplify before solving for $x$ .

$x ^ { 2 } + 8 x - 33 = 0$
Hint (c):
Factor this equation to find the solutions.
Answer (c):
$x=−11$ or $3$

$\frac { 2 } { 3 } x - 12 = 180$
Hint (d):
Multiply each term by $3$ to simplify.

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