 kihanja20

2021-12-26

To solve: $\frac{n+1}{8}-\frac{2-n}{3}=\frac{5}{6}$ levurdondishav4

Step 1
Distributive property is $a\left(b+c\right)=ab+ac$
Calculation:
Given: $\frac{n+1}{8}-\frac{2-n}{3}=\frac{5}{6}$
Multiply by 24 on both sides,
$24\left(\frac{n+1}{8}-\frac{2-n}{3}\right)=\frac{5}{6}×24$
By distributive property,
$24×\left(\frac{n+1}{8}-\frac{2-n}{3}\right)=24×\left(\frac{n+1}{8}\right)-24×\left(\frac{2-n}{3}\right)$
$24×\left(\frac{n+1}{8}-\frac{2-n}{3}\right)=3\left(n+1\right)-8×\left(2-n\right)$
$24×\left(\frac{n+1}{8}-\frac{2-n}{3}\right)=3×n+3×1-8×2-8×-n$
$24×\left(\frac{n+1}{8}-\frac{2-n}{3}\right)=3n+3-16+8n$
$24×\left(\frac{n+1}{8}-\frac{2-n}{3}\right)=11n-13$
$\frac{5}{6}×24=5×4$
$\frac{5}{6}×24=20$
$11n-13=20$
$11n-13+13=20+13$
$11n=33$
Divide by 11 on both sides.
$\frac{11n}{11}=\frac{33}{11}$
$n=3$ Paineow

Step 1
Given: $\frac{n+1}{8}-\left(\frac{2-n}{3}\right)=\frac{5}{6}$
Distribute
$\frac{1}{8}n+\frac{1}{8}+\frac{1}{3}n+\frac{-2}{3}=\frac{5}{6}$
Combine Like Terms
$\left(\frac{1}{8}n+\frac{1}{3}n\right)+\left(\frac{1}{8}+\frac{-2}{3}\right)=\frac{5}{6}$
$\frac{11}{24}n+\frac{-13}{24}=\frac{5}{6}$
Add $\frac{13}{24}$ to both sides.
$\frac{11}{24}n+\frac{-13}{24}+\frac{13}{24}=\frac{5}{6}+\frac{13}{24}$
$\frac{11}{24}n=\frac{11}{8}$
Multiply both sides by $\frac{24}{11}$
$\left(\frac{24}{11}\right)×\left(\frac{11}{24}n\right)=\left(\frac{24}{11}\right)×\left(\frac{11}{8}\right)$
$n=3$ karton

Step 1
Find Least Common Multiplier of 8, 3, 6: 24
LCM =24
$\frac{n+1}{8}×24-\frac{2-n}{3}×24=\frac{5}{6}×24$
Simplify
$\frac{n+1}{8}×24:\phantom{\rule{1em}{0ex}}3\left(n+1\right)$
Multiply fractions: $a×\frac{b}{c}=\frac{a×b}{c}$
$=\frac{\left(n+1\right)×24}{8}$
Divide the numbers: $\frac{24}{8}=3$
=3(n+1)
Sinplify: $-\frac{2-n}{3}×24$
Multiply fractions:
$=-\frac{\left(2-n\right)×24}{3}$
Divide the numbers: $\frac{24}{3}=8$
$=-8\left(-n+2\right)$
Simplify: $\frac{5}{6}×24$
Convert element to fraction: $24=\frac{24}{1}$
$=\frac{5}{6}×\frac{24}{1}$
Cross - cancel common factor: 6
$=\frac{5}{1}×\frac{4}{1}$
Multiply fractions: $\frac{a}{b}×\frac{c}{d}=\frac{a×c}{b×d}$
$=\frac{5×4}{1×1}$
Multiply the numbers: 5*4=20
$=\frac{20}{1×1}$
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
11n-13+13=20+13
Simplify
11n=33
Divide both sides by 11
$\frac{11n}{11}=\frac{33}{11}$
Simplify: n=3

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