Question

Four plus three eighths x equals seven
solve for x

Answer 1

`\huge\text{Hey there!}`

`\huge\textbf{Question reads:}`

`\large\textsf{Four plus three eighths x equals seven}`

`\huge\textbf{Equation should look like:}`

`\mathtt{4 + (3)/(8)x = 7}`

`\huge\textbf{How will we solve for it?}`

`\mathtt{4 + (3)/(8)x = 7}`

`\mathtt{(3)/(8)x + 4= 7}`

`\large\text{SUBTRACT 4 to BOTH SIDES:}`

`\mathtt{(3)/(8)x + 4 - 4 = 7 - 4}`

`\large\text{CANCEL out: 4 } \rm{-}\large\text{ 4 because it gives you 0.}`

`\large\text{KEEP: 7 }\rm{-}\large\text{ 4 because it help us solve for the x}-\large\text{value.}`

`\mathtt{(3)/(8)x = 7 - 4}`

`\mathtt{(3)/(8)x = 3}`

`\large\text{MULTIPLY }\rm{(8)/(3)\large\text{ to BOTH SIDES:}`

`\mathtt{(3)/(8)x*(8)/(3) = 3*(8)/(3)}`

`\large\text{CANCEL out: }\rm{(3)/(8)*(8)/(3)\large\text{ because it gives you 1.}`

`\large\text{KEEP: }\rm{3*(8)/(3)\large\text{ because it gives the x}\rm{-}\large\text{value.}`

`\mathtt{x= 3*(8)/(3)}`

`\mathtt{x= (3)/(1)*(8)/(3)}`

`\mathtt{x = (3*8)/(1*3)}`

`\mathtt{x = (24)/(3)}`

`\mathtt{x = 24/3}`

`\mathtt{x = 8}`

`\huge\textbf{What is the overall answer?}`

`\huge\boxed{\mathtt{x = 8}}\huge\checkmark`

~
`\frak{Amphitrite1040:)}`

Answer 2

`\large\boxed{\mathtt{x=8}}`

Explanation:

`\textsf{For this problem, we are asked to solve for x.}`

`\textsf{Note that our equation is in word form, let's change it into numerical form.}`

`\large \tt { {4 \ plus \ 3 \ eighths \ x \ equals \ seven. } \atop {4+ (3)/(8) x = 7. } }`

`\large\underline{\textsf{Solving;}}`

`\textsf{Our goal is to find x. We should isolate x where its alone on the left side.}`

`\underline{\textsf{How?}}`

`\textsf{Simply subtract 4 from both sides to isolate x.}`

`\large\underline{\textsf{Isolating x;}}`

`\tt 4 - 4 + (3)/(8) x = 7 - 4`

`\underline{\textsf{We should have;}}`

`\tt (3)/(8) x = 3`

`\textsf{We don't know the value of x yet. We only know 3/8 of x.}`

`\textsf{For x to equal 1, multiply both sides of the equation by the \underline{reciprocal} of the fraction.}`

`\large\underline{\textsf{What is a Reciprocal?}}`

`\textsf{A Reciprocal is a \underline{fraction} where the Numerator and the Denominator \underline{flip}.}`

`\underline{\textsf{For example;}}`

`\large \tt {Flip \ the \ Numerator \ and \ the \ Denominator.} \atop {The \ Reciprocal \ of \ (5)/(4) \ is \ (4)/(5).}`

`\large\underline{\textsf{Find the Reciprocal of} \ (3)/(8);}`

`\tt{ The \ Reciprocal \ of \ (3)/(8) \ is \ (8)/(3).}`

`\underline{\textsf{Multiply;}}`

`\tt (8)/(3) * (3)/(8) x = 3 * (8)/(3)`

`\large\boxed{\mathtt{x=8}}`