Question

practice solve each equation. show your work, and check your answer.
#1 ( 8x + 5 = 6x + 1 )
#2 ( x - 1 = -5 - x )
#3 ( 10x + 18 = 8x + 4 )
#4 ( 8 + 4x = 9x - 7 )
#5 ( 5x - 7 = 2(x + 1) )
#6 ( 3(x + 12) = 8 - 4x )
#7 ( 9x = 6(x + 4) )
#8 ( 40 + 14x = 2(-4x ) (incomplete, likely a typo but main equations are the numbered ones)

Explanation:

#1 Step1: Subtract $6x$ from both sides

$8x - 6x + 5 = 6x - 6x + 1$
$2x + 5 = 1$

#1 Step2: Subtract 5 from both sides

$2x + 5 - 5 = 1 - 5$
$2x = -4$

#1 Step3: Divide by 2 on both sides

$x = \frac{-4}{2}$
$x = -2$

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#2 Step1: Add $x$ to both sides

$x + x - 1 = -5 - x + x$
$2x - 1 = -5$

#2 Step2: Add 1 to both sides

$2x - 1 + 1 = -5 + 1$
$2x = -4$

#2 Step3: Divide by 2 on both sides

$x = \frac{-4}{2}$
$x = -2$

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#3 Step1: Subtract $8x$ from both sides

$10x - 8x + 18 = 8x - 8x + 4$
$2x + 18 = 4$

#3 Step2: Subtract 18 from both sides

$2x + 18 - 18 = 4 - 18$
$2x = -14$

#3 Step3: Divide by 2 on both sides

$x = \frac{-14}{2}$
$x = -7$

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#4 Step1: Subtract $4x$ from both sides

$8 + 4x - 4x = 9x - 4x - 7$
$8 = 5x - 7$

#4 Step2: Add 7 to both sides

$8 + 7 = 5x - 7 + 7$
$15 = 5x$

#4 Step3: Divide by 5 on both sides

$x = \frac{15}{5}$
$x = 3$

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#5 Step1: Expand right-hand side

$5x - 7 = 2x + 2$

#5 Step2: Subtract $2x$ from both sides

$5x - 2x - 7 = 2x - 2x + 2$
$3x - 7 = 2$

#5 Step3: Add 7 to both sides

$3x - 7 + 7 = 2 + 7$
$3x = 9$

#5 Step4: Divide by 3 on both sides

$x = \frac{9}{3}$
$x = 3$

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#6 Step1: Expand left-hand side

$3x + 36 = 8 - 4x$

#6 Step2: Add $4x$ to both sides

$3x + 4x + 36 = 8 - 4x + 4x$
$7x + 36 = 8$

#6 Step3: Subtract 36 from both sides

$7x + 36 - 36 = 8 - 36$
$7x = -28$

#6 Step4: Divide by 7 on both sides

$x = \frac{-28}{7}$
$x = -4$

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#7 Step1: Expand right-hand side

$9x = 6x + 24$

#7 Step2: Subtract $6x$ from both sides

$9x - 6x = 6x - 6x + 24$
$3x = 24$

#7 Step3: Divide by 3 on both sides

$x = \frac{24}{3}$
$x = 8$

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#8 Step1: Expand right-hand side

$40 + 14x = -8x$

#8 Step2: Add $8x$ to both sides

$40 + 14x + 8x = -8x + 8x$
$40 + 22x = 0$

#8 Step3: Subtract 40 from both sides

$22x = -40$

#8 Step4: Divide by 22 on both sides

$x = \frac{-40}{22} = \frac{-20}{11}$

Answer:

1. $x = -2$
2. $x = -2$
3. $x = -7$
4. $x = 3$
5. $x = 3$
6. $x = -4$
7. $x = 8$
8. $x = -\frac{20}{11}$