QuestionSolve for $x$ in the equation $a(100+x)=b(100-2)$ .

Studdy Solution

STEP 1

Assumptions1. The equation given is $a(100+x)=b(100-)$ . $a$ and $b$ are constants3. $x$ is the variable we are solving for

STEP 2

First, we need to simplify the equation. We can do this by distributing $a$ and $b$ to the terms inside the parentheses.
$a \cdot100 + a \cdot x = b \cdot100 -2 \cdot b$

STEP 3

Now, we can simplify the equation further by multiplying the constants with the variables.
$100a + ax =100b -2b$

STEP 4

We want to isolate $x$ to one side of the equation. We can do this by subtracting $100a$ from both sides.
$ax =100b -2b -100a$

STEP 5

Now, we can simplify the equation further by combining like terms on the right side.
$ax =98b -100a$

STEP 6

Finally, we can solve for $x$ by dividing both sides of the equation by $a$ .
$x = \frac{98b -100a}{a}$ So, the solution to the equation $a(100+x)=b(100-2)$ is $x = \frac{98b -100a}{a}$ .

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QuestionSolve for $x$ in the equation $a(100+x)=b(100-2)$ .

Studdy Solution

STEP 1

Assumptions1. The equation given is $a(100+x)=b(100-)$ . $a$ and $b$ are constants3. $x$ is the variable we are solving for

STEP 2

First, we need to simplify the equation. We can do this by distributing $a$ and $b$ to the terms inside the parentheses.
$a \cdot100 + a \cdot x = b \cdot100 -2 \cdot b$

STEP 3

Now, we can simplify the equation further by multiplying the constants with the variables.
$100a + ax =100b -2b$

STEP 4

We want to isolate $x$ to one side of the equation. We can do this by subtracting $100a$ from both sides.
$ax =100b -2b -100a$

STEP 5

Now, we can simplify the equation further by combining like terms on the right side.
$ax =98b -100a$

STEP 6

Finally, we can solve for $x$ by dividing both sides of the equation by $a$ .
$x = \frac{98b -100a}{a}$ So, the solution to the equation $a(100+x)=b(100-2)$ is $x = \frac{98b -100a}{a}$ .

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QuestionSolve for xxx in the equation a(100+x)=b(100−2)a(100+x)=b(100-2)a(100+x)=b(100−2).

Studdy Solution

STEP 1

Assumptions1. The equation given is a(100+x)=b(100−)a(100+x)=b(100-)a(100+x)=b(100−). aaa and bbb are constants3. xxx is the variable we are solving for

STEP 2

First, we need to simplify the equation. We can do this by distributing aaa and bbb to the terms inside the parentheses.a⋅100+a⋅x=b⋅100−2⋅ba \cdot100 + a \cdot x = b \cdot100 -2 \cdot ba⋅100+a⋅x=b⋅100−2⋅b

STEP 3

Now, we can simplify the equation further by multiplying the constants with the variables.100a+ax=100b−2b100a + ax =100b -2b100a+ax=100b−2b

STEP 4

We want to isolate xxx to one side of the equation. We can do this by subtracting 100a100a100a from both sides.ax=100b−2b−100aax =100b -2b -100aax=100b−2b−100a

STEP 5

Now, we can simplify the equation further by combining like terms on the right side.ax=98b−100aax =98b -100aax=98b−100a

STEP 6

Finally, we can solve for xxx by dividing both sides of the equation by aaa.x=98b−100aax = \frac{98b -100a}{a}x=a98b−100a​So, the solution to the equation a(100+x)=b(100−2)a(100+x)=b(100-2)a(100+x)=b(100−2) is x=98b−100aax = \frac{98b -100a}{a}x=a98b−100a​.

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Studdy solves anything!

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QuestionSolve for $x$ in the equation $a(100+x)=b(100-2)$ .

Assumptions1. The equation given is $a(100+x)=b(100-)$ . $a$ and $b$ are constants3. $x$ is the variable we are solving for

First, we need to simplify the equation. We can do this by distributing $a$ and $b$ to the terms inside the parentheses.
$a \cdot100 + a \cdot x = b \cdot100 -2 \cdot b$

Now, we can simplify the equation further by multiplying the constants with the variables.
$100a + ax =100b -2b$

We want to isolate $x$ to one side of the equation. We can do this by subtracting $100a$ from both sides.
$ax =100b -2b -100a$

Now, we can simplify the equation further by combining like terms on the right side.
$ax =98b -100a$

Finally, we can solve for $x$ by dividing both sides of the equation by $a$ .
$x = \frac{98b -100a}{a}$ So, the solution to the equation $a(100+x)=b(100-2)$ is $x = \frac{98b -100a}{a}$ .