Respuesta :
Answer:
[tex]y=\frac{54}{5}=10\frac{4}{5}[/tex]
Step-by-step explanation:
1. Simplify the expression
[tex]y-\left(7\cdot \left(y-4\right)\right)=-y-26[/tex]
Solve by distributing:
[tex]y-\left(7y+7\cdot -4\right)=-y-26[/tex]
Simplify the arithmetic:
[tex]y-\left(7y-28\right)=-y-26[/tex]
Expand the parentheses:
[tex]y-7y+28=-y-26[/tex]
Simplify the arithmetic:
[tex]-6y+28=-y-26[/tex]
2. Group all y terms on the left side of the equation
[tex]-6y+28=-y-26[/tex]
Add y to both sides:
[tex]-6y+28+y=-y-26+y[/tex]
Group like terms:
[tex]-6y+y+28=-y-26+y[/tex]
Simplify the arithmetic:
[tex]-5y+28=-y-26+y[/tex]
Group like terms:
[tex]-5y+28=-y+y-26[/tex]
Simplify the arithmetic:
[tex]-5y+28=-26[/tex]
3. Group all constants on the right side of the equation
[tex]-5y+28=-26[/tex]
Subtract 28 from both sides:
[tex]-5y+28-28=-26-28[/tex]
Simplify the arithmetic:
[tex]-5y=-26-28[/tex]
Simplify the arithmetic:
[tex]-5y=-54[/tex]
4. Isolate the y
[tex]-5y=-54[/tex]
Divide both sides by -5:
[tex]\frac{-5y}{-5}=\frac{-54}{-5}[/tex]
Cancel out the negatives:
[tex]\frac{5y}{5}=\frac{-54}{-5}[/tex]
Simplify the fraction:
[tex]y=\frac{-54}{-5}[/tex]
Cancel out the negatives:
[tex]y=\frac{54}{5}[/tex]
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Why learn this
- Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends? Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.
Terms and topics
- Linear equations with one unknown
Learn more:
- https://brainly.com/question/1632711
Answer: y = 54/5
Step-by-step explanation:
[tex]$Solve for $y$ :$y-7(y-4)=-y-26$$\begin{aligned}&-7(y-4)=-7 y+28 \\&y+-7 y+28=-y-26\end{aligned}$$\begin{aligned}&y-7 y=-6 y: \\&-6 y+28=-y-26\end{aligned}$Add $y$ to both sides:$y-6 y+28=(y-y)-26$$\begin{aligned}&y-y=0 \\&y-6 y+28=-26\end{aligned}$Grouping like terms, $y-6 y+28=(-6 y+y)+28$ : $(-6 y+y)+28=-26$$\begin{aligned}&y-6 y=-5 y: \\&-5 y+28=-26\end{aligned}$Subtract 28 from both sides:$(28-28)-5 y=-28-26$[/tex][tex]$\begin{aligned}&28-28=0 \\&-5 y=-28-26\end{aligned}$[/tex]
[tex]$\begin{aligned}&-28-26=-54 \\&-5 y=-54\end{aligned}[/tex]
[tex]$Divide both sides of $-5 y=-54$ by $-5$ :$\frac{-5 y}{-5}=\frac{-54}{-5}$$\begin{aligned}&\frac{-5}{-5}=1 \\&y=\frac{-54}{-5}\end{aligned}[/tex]
[tex]$Multiply numerator and denominator of $\frac{-54}{-5}$ by $-1$ :\\Answer:$y=\frac{54}{5}$[/tex]
