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Solve the following equations using balancing method. 1. 2x = -10 2. 2y = 10 3. x/9 = -3 4. 8 = p/4 5. 8q − 16 = 0 6. z − 8 = 0 7. 2x/8 = 5 8. -8−5d = 7 9. m+10 = 16 10. -k+7 = 12
Mathematics
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Step-by-step solution
14 stepsHere are the solutions to the equations using the balancing method:
Divide both sides by 2.
$$ \frac{2x}{2} = \frac{-10}{2} $$ $$ x = -5 $$ The solution is $\boxed{x = -5}$.2.
Divide both sides by 2.
$$ \frac{2y}{2} = \frac{10}{2} $$ $$ y = 5 $$ The solution is $\boxed{y = 5}$.3.
Multiply both sides by 9.
$$ \frac{x}{9} \times 9 = -3 \times 9 $$ $$ x = -27 $$ The solution is $\boxed{x = -27}$.4.
Multiply both sides by 4.
$$ 8 \times 4 = \frac{p}{4} \times 4 $$ $$ 32 = p $$ The solution is $\boxed{p = 32}$.5.
Add 16 to both sides.
$$ 8q - 16 + 16 = 0 + 16 $$ $$ 8q = 16 $$Divide both sides by 8.
$$ \frac{8q}{8} = \frac{16}{8} $$ $$ q = 2 $$ The solution is $\boxed{q = 2}$.6.
Add 8 to both sides.
$$ z - 8 + 8 = 0 + 8 $$ $$ z = 8 $$ The solution is $\boxed{z = 8}$.7.
Multiply both sides by 8.
$$ \frac{2x}{8} \times 8 = 5 \times 8 $$ $$ 2x = 40 $$Divide both sides by 2.
$$ \frac{2x}{2} = \frac{40}{2} $$ $$ x = 20 $$ The solution is $\boxed{x = 20}$.8.
Add 8 to both sides.
$$ -8 - 5d + 8 = 7 + 8 $$ $$ -5d = 15 $$Divide both sides by -5.
$$ \frac{-5d}{-5} = \frac{15}{-5} $$ $$ d = -3 $$ The solution is $\boxed{d = -3}$.9.
Subtract 10 from both sides.
$$ m + 10 - 10 = 16 - 10 $$ $$ m = 6 $$ The solution is $\boxed{m = 6}$.10.
Subtract 7 from both sides.
$$ -k + 7 - 7 = 12 - 7 $$ $$ -k = 5 $$Multiply both sides by -1.
$$ -k \times (-1) = 5 \times (-1) $$ $$ k = -5 $$ The solution is $\boxed{k = -5}$.
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