The equivalent options are:
"One-sixth x + 47" ⇒ 2nd
"1 and two-thirds x + 35 minus 1 and one-half x + 12" ⇒ 3rd
"5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)" ⇒ 4th
Step-by-step explanation:
The expression is: 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) to find the equivalent to it:
Multiply the bracket ( [tex]\frac{1}{3}[/tex] x + 7) by 5
∵ 5( [tex]\frac{1}{3}[/tex] x + 7) = 5(
Multiply the bracket ( [tex]\frac{1}{2}[/tex] x - 4) by - 3
∵ -3( [tex]\frac{1}{2}[/tex] x - 4) = -3(
∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = [tex]\frac{5}{3}[/tex] x + 35 - [tex]\frac{3}{2}[/tex] x + 12
Add the like terms
∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = ( [tex]\frac{5}{3}[/tex] x - [tex]\frac{3}{2}[/tex] x) + (35 + 12)
To add fraction with different denominators find the LCM of the two denominators and change them by it, then divide the LCM by each denominator and multiply the quotient by the corresponding numerator
∵ LCM of 3 and 2 is 6
∵ 6 ÷ 3 = 2, then multiply 5 by 2
∴ [tex]\frac{5}{3}[/tex] = [tex]\frac{10}{6}[/tex]
∵ 6 ÷ 2 = 3, then multiply 3 by 3
∴ [tex]\frac{3}{2}[/tex] = [tex]\frac{9}{6}[/tex]
∴ ( [tex]\frac{5}{3}[/tex] x - [tex]\frac{3}{2}[/tex] x) = [tex]\frac{10}{6}[/tex] x - [tex]\frac{9}{6}[/tex] x = [tex]\frac{1}{6}[/tex] x
∵ 35 + 12 = 47
∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = [tex]\frac{1}{6}[/tex] x + 47
The 1st option is "One-sixth x + 47"
In the step 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = [tex]\frac{5}{3}[/tex] x + 35 - [tex]\frac{3}{2}[/tex] x + 12
∵ [tex]\frac{5}{3}[/tex] = [tex]1\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex] = [tex]1\frac{1}{2}[/tex]
∴ [tex]\frac{5}{3}[/tex] x + 35 - [tex]\frac{3}{2}[/tex] x + 12 = [tex]1\frac{2}{3}[/tex] x + 35 - [tex]1\frac{1}{2}[/tex] x + 12
∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = [tex]1\frac{2}{3}[/tex] x + 35 - [tex]1\frac{1}{2}[/tex] x + 12
The 2nd option is "1 and two-thirds x + 35 minus 1 and one-half x + 12"
∵ 5( [tex]\frac{1}{3}[/tex] x + 7) = 5(
∵ -3( [tex]\frac{1}{2}[/tex] x - 4) = -3(
∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = 5(
The 3rd option is "5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)"
Learn more:
You can learn more about fractions in brainly.com/question/1757979
#LearnwithBrainly
Answer:
[tex]5(\frac{1}{3}x)+5(7)-3 (\frac{1}{2}x)+(3)(4)[/tex]
[tex]1\frac{2}{3}x+35-1\frac{1}{2}x+ 12[/tex]
[tex]\frac{1}{6}x+47[/tex]
Step-by-step explanation:
The given expression is [tex]5(\frac{1}{3}x+7)-3 (\frac{1}{2}x- 4)[/tex]
We expand to get:
[tex]5(\frac{1}{3}x)+5(7)-3 (\frac{1}{2}x)+(3)(4)[/tex]
[tex]\frac{5}{3}x+35-\frac{3}{2}x+ 12[/tex]
As mixed number coefficients:
[tex]1\frac{2}{3}x+35-1\frac{1}{2}x+ 12[/tex]
This simplifies to:
[tex]\frac{1}{6}x+47[/tex]
