Question

What is the solution of ?Formula1" title="\frac{5}{2} x-7=\frac{3}{4} x+14" alt="\frac{5}{2} x-7=\frac{3}{4} x+14" align="absmiddle" class="latex-formula">

Answer 1

Combine the terms by multiplying into a single fraction.

$\bf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 }$

Find the common denominator.

$\bf{\dfrac{5x}{2}-7=\dfrac{3}{4}x+14 }$

Combine fractions with the lowest common denominator.

$\bf{\dfrac{5x(-7)}{2}=\dfrac{3}{4}x+14 }$

Multiply the numbers.

$\bf{\dfrac{5x-14}{2}=\dfrac{3}{4}x+14 }$

Combine the multiplied terms into a single fraction

$\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+14 }$

Find the common denominator.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+\dfrac{4\cdot14}{4} }$

Combine fractions with the lowest common denominator.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x+4\cdot14}{4} }$

Multiply the numbers.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x+56}{4} }$

Eliminate the denominators of the fractions.

$\bf{4\cdot\dfrac{5x-14}{2}=4\cdot\dfrac{3x+56}{4} }$

Cancel the multiplied terms that are in the denominator.

$\bf{2(5x-14)=3x+56}$

To distribute.

$\bf{10x-28=3x+56 }$

Add 28 to both sides.

$\bf{10x-28+28=3x+56+28 }$

Simplify

$\bf{10x=3x+84 }$

Subtract 3x from both sides.

$\bf{10x-3x=3x+84-3x }$

Simplify

$\bf{7x=84 }$

Divide both sides by the same factor.

$\bf{x=\dfrac{84}{7} }$

Simplify

$\bf{x=12 \ \ \ === > \ \ \ Answer}$

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Verification

Let x=12.

1. $\bf{\dfrac{5}{2}\times12-7=\dfrac{3}{4}\times12+14 }$
2. $\bf{\dfrac{5\times12}{2}-7=\dfrac{3}{4}\times12+14 }$
3. $\bf{\dfrac{60}{2}-7=\dfrac{3}{4}\times12+14 }$
4. $\bf{30-7=\dfrac{3}{4}\times12+14 }$
5. $\bf{30-7=\dfrac{3\times12}{4}+14 }$
6. $\bf{30-7=\dfrac{36}{4}+14 }$
7. $\bf{30-7=9+14 }$
8. $\bf{23=9+14 }$
9. $\bf{23=23}$

Checked ✅