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1-36.

Solve the following linear equations.

$8x+1=−x−1$
Step 1(a):
Subtract $1$ from each side.
$8x+1=−x−1$
$\ \ \ \ −1\ \ \ \ \ \ \ \ \ \ \ −1$
$8x=−x−2$
Step 2(a):
Add $x$ to both sides.

$8x=−x−2$
$+x\ \ \ +x$
$9x=−2$
Step 3(a):
Divide both sides by $9$
$\frac{9x}{9}=\frac{-2}{9}$
Answer(a):
$x=-\frac{2}{9}$

$−4x−3=$ $3x−4−7x$
Step 1(b):
Combine like terms on either side of the equation.
$−4x−3=−4x−4$
Step 2(b):
Add $3$ to both sides.

$−4x−3=−4x−4$
$\ \ \ \ \ \ \ +3\ \ \ \ \ \ \ \ \ \ \ \ \ +3$
$−4x=−4x−1$
Step 3(b):
Add $4x$ to both sides.
$−4x=−4x−1$
$+4x\ \ \ \ +4x$
$0=1$
Answer(b):
No solution. Do you see why?

$4−5x=1+6x$
Hint(c):
Refer to part (a).

$7−x+3=$ $9x+10$
Hint(d):
Refer to part (b).

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