2022-01-10

3/4x+2=9/10 No decimals

nick1337

Solve for x:
$\frac{3x}{4}+2=\frac{9}{10}$

Put the fractions in $\frac{3x}{4}+2$ over a common denominator.
Put each term in $\frac{3x}{4}+2$ over the common denominator 4: $\frac{3x}{4}+2=\frac{3x}{4}+\frac{8}{4}:$
$\left(\frac{3x}{4}+\frac{8}{4}\right)=\frac{9}{10}$

Combine$\frac{3x}{4}+\frac{8}{4}$ into a single fraction.
$\frac{3x}{4}+\frac{8}{4}=\frac{3x+8}{4}:$
$\left(\frac{1}{4}\left(3x+8\right)\right)=\frac{9}{10}$

Multiply both sides by a constant to simplify the equation.
Multiply both sides of $\frac{3x+8}{4}=\frac{9}{10}$ by 4:
$\frac{4\left(3x+8\right)}{4}=4×\frac{9}{10}$

Express $4×\frac{9}{10}$ as a single fraction.
$4×\frac{9}{10}=\frac{4×9}{10}:$
$\frac{4\left(3x+8\right)}{4}=\frac{4×9}{10}$

Cancel common terms in the numerator and denominator of $\frac{4\left(3x+8\right)}{4}.$
$\frac{4\left(3x+8\right)}{4}=\frac{4}{4}×\left(3x+8\right)=3x+8:$
$\left(3x+8\right)=\frac{4×9}{10}$

In $\frac{4×9}{10}$, the numbers 4 in the numerator and 10 in the denominator have gcd greater than one.
The gcd of 4 and 10 is 2, so $\frac{4×9}{10}=\frac{\left(2×2\right)9}{2×5}=\frac{2}{2}×\frac{2×9}{5}=\frac{2×9}{5}:$
$3x+8=\frac{2×9}{5}$

Multiply 2 and 9 together.
$2×9=18:$
$3x+8=\frac{18}{5}$

Isolate terms with x to the left hand side.
Subtract 8 from both sides:
$3x+\left(8-8\right)=\frac{18}{5}-8$

Look for the difference of two identical terms.
$8-8=0:$
$3x=\frac{18}{5}-8$

Put the fractions in 18/5 - 8 over a common denominator.
Put $\frac{18}{5}-8$ over the common denominator 5. $\frac{18}{5}-8=\frac{18}{5}+\frac{5\left(-8\right)}{5}:$
$3x=\left(\frac{18}{5}-\frac{8×5}{5}\right)$

Multiply 5 and -8 together.
$5\left(-8\right)=-40:$

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