Math

QuestionSolve the equation: 7(2+5v)=3v+147(2+5 v)=3 v+14.

Studdy Solution

STEP 1

Assumptions1. The equation given is 7(+5v)=3v+147(+5 v)=3 v+14 . We are solving for the variable vv

STEP 2

First, we need to distribute the 77 to both terms inside the parentheses on the left side of the equation.
7(2+5v)=7×2+7×5v7(2+5 v) =7 \times2 +7 \times5v

STEP 3

Now, calculate the multiplication to simplify the left side of the equation.
7×2+7×5v=14+35v7 \times2 +7 \times5v =14 +35v

STEP 4

So, the equation becomes14+35v=3v+1414 +35v =3v +14

STEP 5

Next, we need to get all terms with vv on one side of the equation and the constants on the other side. We can do this by subtracting 3v3v from both sides of the equation.
14+35v3v=3v+143v14 +35v -3v =3v +14 -3v

STEP 6

implify the equation.
14+32v=1414 +32v =14

STEP 7

Now, subtract 1414 from both sides of the equation to isolate the vv term.
14+32v14=141414 +32v -14 =14 -14

STEP 8

implify the equation.
32v=032v =0

STEP 9

Finally, divide both sides of the equation by 3232 to solve for vv.
v=/32v =/32

STEP 10

implify to find the value of vv.
v=0v =0So, the solution to the equation is v=0v =0.

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