Question

Can someone help me with one pleaseT (ToT)

Answer 1

Step-by-step explanation:

can't you see it ?

the goal is always to get the variable on one side, and everything else on the other side.

1. step : add 1 to both sides to get rid of the free constant "-1" on the side of the variable.

2. step : multiply both sides by -2 to get rid of the "-1/2" factor that binds 5x and -8 into one term.

3. step : add 8 to both sides to get rid of the now free constant "-8" on the side of the variable.

4. step : divide both sides by 5 to finally have only the variable on the left side giving us the solution of the equation.

remember, we always have to do every change on both sides of the equation to keep the original balance and information of the equation.

Answer 2

Answer:

Add 1 to both sides.

Multiply both sides by -2.

Add 8 to both sides.

Divide both sides by 5.

Step-by-step explanation:

Step 1

$-\dfrac{1}{2}(5x-8)-1=6\quad \quad \textsf{Write the equation.}$

Step 2

$-\dfrac{1}{2}(5x-8)=7 \quad \quad \textsf{Add 1 to both sides.}$

This is called the Addition Property of Equality.  When the same number is added to both sides of an equation, the two sides remain equal.

$\implies -\dfrac{1}{2}(5x-8)-1+1=6+1$

$\implies -\dfrac{1}{2}(5x-8)=7$

Step 3

$5x-8=-14 \quad \quad \textsf{Multiply both sides by -2.}$

This is called the Multiplication Property of Equality.  When both sides of an equation are multiplied by the same number, the two sides remain equal.

$\implies -2 \cdot -\dfrac{1}{2}(5x-8)=-2 \cdot 7$

$\implies 5x-8=-14$

Step 4

$5x=-6 \quad \quad \textsf{Add 8 to both sides.}$

This is called the Addition Property of Equality.  When the same number is added to both sides of an equation, the two sides remain equal.

$\implies 5x-8+8=-14+8$

$\implies 5x=-6$

Step 5

$x=-\dfrac{6}{5} \quad \quad \textsf{Divide both sides by 5.}$

This is called the Division Property of Equality.  When both sides of an equation are divided by the same number, the two sides remain equal.

$\implies \dfrac{5x}{5}=\dfrac{-6}{5}$

$\implies x=\dfrac{-6}{5}$

Conclusion

$\begin{aligned}-\dfrac{1}{2}(5x-8)-1 & =6 & \quad \quad& \textsf{Write the equation.}\\\\-\dfrac{1}{2}(5x-8) & =7 & & \boxed{\textsf{Add 1 to both sides.}}\\\\5x-8 & =-14 & & \boxed{\textsf{Multiply both sides by -2.}}\\\\5x & =-6 & & \boxed{\textsf{Add 8 to both sides.}}\\\\x & =-\dfrac{6}{5} & & \boxed{\textsf{Divide both sides by 5.}}\\\end{aligned}$

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