Math

Question Solve the linear equation y+5(2y7)=9y + 5(2y - 7) = 9 for the variable yy.

Studdy Solution

STEP 1

Assumptions1. The equation is y+5(y7)=9y+5 \cdot( y-7)=9 . We are solving for yy

STEP 2

First, we need to distribute the 55 to both terms inside the parentheses.
y+5(2y7)=9y+52y57=9y+5 \cdot(2 y-7)=9 \Rightarrow y +5 \cdot2y -5 \cdot7 =9

STEP 3

Next, simplify the equation.
y+10y35=9y +10y -35 =9

STEP 4

Combine like terms on the left side of the equation.
11y35=911y -35 =9

STEP 5

To isolate yy, we first add 3535 to both sides of the equation.
11y35+35=9+3511y=4411y -35 +35 =9 +35 \Rightarrow11y =44

STEP 6

Finally, divide both sides of the equation by 1111 to solve for yy.
y=44/11y =44 /11

STEP 7

Calculate the value of yy.
y=44/11=4y =44 /11 =4So, the solution to the equation y+5(2y7)=9y+5 \cdot(2 y-7)=9 is y=4y =4.

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