Respuesta :
Combine the terms by multiplying into a single fraction.
[tex]\bf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 }[/tex]
Find the common denominator.
[tex]\bf{\dfrac{5x}{2}-7=\dfrac{3}{4}x+14 }[/tex]
Combine fractions with the lowest common denominator.
[tex]\bf{\dfrac{5x(-7)}{2}=\dfrac{3}{4}x+14 }[/tex]
Multiply the numbers.
[tex]\bf{\dfrac{5x-14}{2}=\dfrac{3}{4}x+14 }[/tex]
Combine the multiplied terms into a single fraction
[tex]\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+14 }[/tex]
Find the common denominator.
[tex]\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+\dfrac{4\cdot14}{4} }[/tex]
Combine fractions with the lowest common denominator.
[tex]\bf{\dfrac{5x-14}{2}=\dfrac{3x+4\cdot14}{4} }[/tex]
Multiply the numbers.
[tex]\bf{\dfrac{5x-14}{2}=\dfrac{3x+56}{4} }[/tex]
Eliminate the denominators of the fractions.
[tex]\bf{4\cdot\dfrac{5x-14}{2}=4\cdot\dfrac{3x+56}{4} }[/tex]
Cancel the multiplied terms that are in the denominator.
[tex]\bf{2(5x-14)=3x+56}[/tex]
To distribute.
[tex]\bf{10x-28=3x+56 }[/tex]
Add 28 to both sides.
[tex]\bf{10x-28+28=3x+56+28 }[/tex]
Simplify
[tex]\bf{10x=3x+84 }[/tex]
Subtract 3x from both sides.
[tex]\bf{10x-3x=3x+84-3x }[/tex]
Simplify
[tex]\bf{7x=84 }[/tex]
Divide both sides by the same factor.
[tex]\bf{x=\dfrac{84}{7} }[/tex]
Simplify
[tex]\bf{x=12 \ \ \ === > \ \ \ Answer}[/tex]
↓
Verification
Let x=12.
- [tex]\bf{\dfrac{5}{2}\times12-7=\dfrac{3}{4}\times12+14 }[/tex]
- [tex]\bf{\dfrac{5\times12}{2}-7=\dfrac{3}{4}\times12+14 }[/tex]
- [tex]\bf{\dfrac{60}{2}-7=\dfrac{3}{4}\times12+14 }[/tex]
- [tex]\bf{30-7=\dfrac{3}{4}\times12+14 }[/tex]
- [tex]\bf{30-7=\dfrac{3\times12}{4}+14 }[/tex]
- [tex]\bf{30-7=\dfrac{36}{4}+14 }[/tex]
- [tex]\bf{30-7=9+14 }[/tex]
- [tex]\bf{23=9+14 }[/tex]
- [tex]\bf{23=23}[/tex]
Checked ✅
