Question

Solve |3x + 7 = 4x for x.A) Infinitely many solutionsB) 7 and -7C) No solutionOD) -7 or 1

Answer 1

The given equation is

`\lvert{3x+7}\rvert=4x`

We will solve it in this way

`3x+7=4x,3x+7=-4x`

For the 1st equation

`3x+7=4x`

Subtract 7 from each side

`\begin{gathered} 3x+7-7=4x-7 \\ 3x=4x-7 \end{gathered}`

Subtract 4x from both sides

`\begin{gathered} 3x-4x=4x-4x-7 \\ -x=-7 \\ x=7 \end{gathered}`

For the 2nd equation

`3x+7=-4x`

Subtract 3x from both sides

`\begin{gathered} 3x-3x+7=-4x-3x \\ 7=-7x \end{gathered}`

Divide both sides by -7

`\begin{gathered} (7)/(-7)=(-7x)/(-7) \\ -1=x \end{gathered}`

The solutions are

7, -1

The answer should be B