To solve: n+18−2−n3=56

Question

levurdondishav4 · Accepted Answer

Step 1  Distributive property is a(b+c)=ab+ac  Calculation:  Given: n+18−2−n3=56  Multiply by 24 on both sides,  24(n+18−2−n3)=56×24  By distributive property,  24×(n+18−2−n3)=24×(n+18)−24×(2−n3)  24×(n+18−2−n3)=3(n+1)−8×(2−n)  24×(n+18−2−n3)=3×n+3×1−8×2−8×−n  24×(n+18−2−n3)=3n+3−16+8n  24×(n+18−2−n3)=11n−13  56×24=5×4  56×24=20  11n−13=20  Add +13 on both sides,  11n−13+13=20+13  11n=33  Divide by 11 on both sides.  11n11=3311  n=3

Paineow · Accepted Answer

Step 1  Given: n+18−(2−n3)=56  Distribute  18n+18+13n+−23=56  Combine Like Terms  (18n+13n)+(18+−23)=56  1124n+−1324=56  Add 1324 to both sides.  1124n+−1324+1324=56+1324  1124n=118  Multiply both sides by 2411  (2411)×(1124n)=(2411)×(118)  n=3

karton · Accepted Answer

Step 1
Find Least Common Multiplier of 8, 3, 6: 24
LCM =24
$\frac{n + 1}{8} \times 24 - \frac{2 - n}{3} \times 24 = \frac{5}{6} \times 24$
Simplify
$\frac{n + 1}{8} \times 24 : 3 (n + 1)$
Multiply fractions: $a \times \frac{b}{c} = \frac{a \times b}{c}$
$= \frac{(n + 1) \times 24}{8}$
Divide the numbers: $\frac{24}{8} = 3$
=3(n+1)
Sinplify: $- \frac{2 - n}{3} \times 24$
Multiply fractions:
$= - \frac{(2 - n) \times 24}{3}$
Divide the numbers: $\frac{24}{3} = 8$
$= - 8 (- n + 2)$
Simplify: $\frac{5}{6} \times 24$
Convert element to fraction: $24 = \frac{24}{1}$
$= \frac{5}{6} \times \frac{24}{1}$
Cross - cancel common factor: 6
$= \frac{5}{1} \times \frac{4}{1}$
Multiply fractions: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$
$= \frac{5 \times 4}{1 \times 1}$
Multiply the numbers: 5*4=20
$= \frac{20}{1 \times 1}$
Multiply the numbers: 1*1=1
$= \frac{20}{1}$
Apply rule $\frac{a}{1} = a$
=20
3(n+1)-8(-n+2)=20
Step 2
Expand P3(n+1)-8(-n+2)

=3n+3-8(-n+2)
=3n+3+8n-16
=11n-13
11n-13=20
Add 13 to both sides
11n-13+13=20+13
Simplify
11n=33
Divide both sides by 11
$\frac{11 n}{11} = \frac{33}{11}$
Simplify: n=3

To solve: \frac{n+1}{8}-\frac{2-n}{3}=\frac{5}{6}

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