QuestionSolve for $x$ in the equation $-25=\frac{1}{2}(10 x-2)+3 x$ .

Studdy Solution

STEP 1

Assumptions1. The equation given is $-25=\frac{1}{}(10 x-)+3 x$ . The equation is linear and has only one variable, $x$
3. The equation can be solved by isolating $x$ on one side of the equation

STEP 2

First, we need to simplify the equation. We can do this by distributing the $\frac{1}{2}$ to both terms in the parentheses.
$-25=\frac{1}{2} \cdot10x - \frac{1}{2} \cdot2 +x$

STEP 3

implify the equation further by performing the multiplication.
$-25=5x -1 +3x$

STEP 4

Combine like terms on the right side of the equation.
$-25=8x -1$

STEP 5

To isolate $x$ , first add1 to both sides of the equation.
$-25 +1 =8x -1 +1$

STEP 6

implify both sides of the equation.
$-24 =8x$

STEP 7

Finally, divide both sides of the equation by to solve for $x$ .
$\frac{-24}{} = \frac{x}{}$

STEP 8

implify both sides of the equation to find the value of $x$ .
$x = -3$ So, the solution to the equation $-25=\frac{1}{2}(10 x-2)+3 x$ is $x = -3$ .

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QuestionSolve for $x$ in the equation $-25=\frac{1}{2}(10 x-2)+3 x$ .

Studdy Solution

STEP 1

Assumptions1. The equation given is $-25=\frac{1}{}(10 x-)+3 x$ . The equation is linear and has only one variable, $x$
3. The equation can be solved by isolating $x$ on one side of the equation

STEP 2

First, we need to simplify the equation. We can do this by distributing the $\frac{1}{2}$ to both terms in the parentheses.
$-25=\frac{1}{2} \cdot10x - \frac{1}{2} \cdot2 +x$

STEP 3

implify the equation further by performing the multiplication.
$-25=5x -1 +3x$

STEP 4

Combine like terms on the right side of the equation.
$-25=8x -1$

STEP 5

To isolate $x$ , first add1 to both sides of the equation.
$-25 +1 =8x -1 +1$

STEP 6

implify both sides of the equation.
$-24 =8x$

STEP 7

Finally, divide both sides of the equation by to solve for $x$ .
$\frac{-24}{} = \frac{x}{}$

STEP 8

implify both sides of the equation to find the value of $x$ .
$x = -3$ So, the solution to the equation $-25=\frac{1}{2}(10 x-2)+3 x$ is $x = -3$ .

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QuestionSolve for xxx in the equation −25=12(10x−2)+3x-25=\frac{1}{2}(10 x-2)+3 x−25=21​(10x−2)+3x.

Studdy Solution

STEP 1

Assumptions1. The equation given is −25=1(10x−)+3x-25=\frac{1}{}(10 x-)+3 x−25=1​(10x−)+3x . The equation is linear and has only one variable, xxx3. The equation can be solved by isolating xxx on one side of the equation

STEP 2

First, we need to simplify the equation. We can do this by distributing the 12\frac{1}{2}21​ to both terms in the parentheses.−25=12⋅10x−12⋅2+x-25=\frac{1}{2} \cdot10x - \frac{1}{2} \cdot2 +x−25=21​⋅10x−21​⋅2+x

STEP 3

implify the equation further by performing the multiplication.−25=5x−1+3x-25=5x -1 +3x−25=5x−1+3x

STEP 4

Combine like terms on the right side of the equation.−25=8x−1-25=8x -1−25=8x−1

STEP 5

To isolate xxx, first add1 to both sides of the equation.−25+1=8x−1+1-25 +1 =8x -1 +1−25+1=8x−1+1

STEP 6

implify both sides of the equation.−24=8x-24 =8x−24=8x

STEP 7

Finally, divide both sides of the equation by to solve for xxx.−24=x\frac{-24}{} = \frac{x}{}−24​=x​

STEP 8

implify both sides of the equation to find the value of xxx.x=−3x = -3x=−3So, the solution to the equation −25=12(10x−2)+3x-25=\frac{1}{2}(10 x-2)+3 x−25=21​(10x−2)+3x is x=−3x = -3x=−3.

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QuestionSolve for $x$ in the equation $-25=\frac{1}{2}(10 x-2)+3 x$ .

Assumptions1. The equation given is $-25=\frac{1}{}(10 x-)+3 x$ . The equation is linear and has only one variable, $x$
3. The equation can be solved by isolating $x$ on one side of the equation

First, we need to simplify the equation. We can do this by distributing the $\frac{1}{2}$ to both terms in the parentheses.
$-25=\frac{1}{2} \cdot10x - \frac{1}{2} \cdot2 +x$

implify the equation further by performing the multiplication.
$-25=5x -1 +3x$

Combine like terms on the right side of the equation.
$-25=8x -1$

To isolate $x$ , first add1 to both sides of the equation.
$-25 +1 =8x -1 +1$

implify both sides of the equation.
$-24 =8x$

Finally, divide both sides of the equation by to solve for $x$ .
$\frac{-24}{} = \frac{x}{}$

implify both sides of the equation to find the value of $x$ .
$x = -3$ So, the solution to the equation $-25=\frac{1}{2}(10 x-2)+3 x$ is $x = -3$ .