QuestionDivide the equation $\frac{1}{2}(x+9)=\frac{7}{8} x$ by $\frac{1}{2}$ . What is the simplified new equation?

Studdy Solution

STEP 1

Assumptions1. The equation is $\frac{1}{}(x+9)=\frac{7}{8} x$ . We need to divide both sides of the equation by $\frac{1}{}$

STEP 2

Divide both sides of the equation by $\frac{1}{2}$ .
$\frac{\frac{1}{2}(x+9)}{\frac{1}{2}}=\frac{\frac{7}{8} x}{\frac{1}{2}}$

STEP 3

implify the left side of the equation. Dividing by $\frac{1}{2}$ is the same as multiplying by $2$ .
$2 \cdot \frac{1}{2}(x+9) = x+9$

STEP 4

implify the right side of the equation. Dividing by $\frac{1}{2}$ is the same as multiplying by $2$ .
$2 \cdot \frac{7}{8} x = \frac{14}{8} x$

STEP 5

implify the fraction on the right side of the equation.
$\frac{14}{8} x = \frac{7}{4} x$ So, the new equation after dividing both sides by $\frac{1}{2}$ and simplifying the fractions is $x+9 = \frac{7}{4} x$

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QuestionDivide the equation $\frac{1}{2}(x+9)=\frac{7}{8} x$ by $\frac{1}{2}$ . What is the simplified new equation?

Studdy Solution

STEP 1

Assumptions1. The equation is $\frac{1}{}(x+9)=\frac{7}{8} x$ . We need to divide both sides of the equation by $\frac{1}{}$

STEP 2

Divide both sides of the equation by $\frac{1}{2}$ .
$\frac{\frac{1}{2}(x+9)}{\frac{1}{2}}=\frac{\frac{7}{8} x}{\frac{1}{2}}$

STEP 3

implify the left side of the equation. Dividing by $\frac{1}{2}$ is the same as multiplying by $2$ .
$2 \cdot \frac{1}{2}(x+9) = x+9$

STEP 4

implify the right side of the equation. Dividing by $\frac{1}{2}$ is the same as multiplying by $2$ .
$2 \cdot \frac{7}{8} x = \frac{14}{8} x$

STEP 5

implify the fraction on the right side of the equation.
$\frac{14}{8} x = \frac{7}{4} x$ So, the new equation after dividing both sides by $\frac{1}{2}$ and simplifying the fractions is $x+9 = \frac{7}{4} x$

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QuestionDivide the equation 12(x+9)=78x\frac{1}{2}(x+9)=\frac{7}{8} x21​(x+9)=87​x by 12\frac{1}{2}21​. What is the simplified new equation?

Studdy Solution

STEP 1

Assumptions1. The equation is 1(x+9)=78x\frac{1}{}(x+9)=\frac{7}{8} x1​(x+9)=87​x . We need to divide both sides of the equation by 1\frac{1}{}1​

STEP 2

Divide both sides of the equation by 12\frac{1}{2}21​.12(x+9)12=78x12\frac{\frac{1}{2}(x+9)}{\frac{1}{2}}=\frac{\frac{7}{8} x}{\frac{1}{2}}21​21​(x+9)​=21​87​x​

STEP 3

implify the left side of the equation. Dividing by 12\frac{1}{2}21​ is the same as multiplying by 222.2⋅12(x+9)=x+92 \cdot \frac{1}{2}(x+9) = x+92⋅21​(x+9)=x+9

STEP 4

implify the right side of the equation. Dividing by 12\frac{1}{2}21​ is the same as multiplying by 222.2⋅78x=148x2 \cdot \frac{7}{8} x = \frac{14}{8} x2⋅87​x=814​x

STEP 5

implify the fraction on the right side of the equation.148x=74x\frac{14}{8} x = \frac{7}{4} x814​x=47​xSo, the new equation after dividing both sides by 12\frac{1}{2}21​ and simplifying the fractions isx+9=74xx+9 = \frac{7}{4} xx+9=47​x

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QuestionDivide the equation $\frac{1}{2}(x+9)=\frac{7}{8} x$ by $\frac{1}{2}$ . What is the simplified new equation?

Assumptions1. The equation is $\frac{1}{}(x+9)=\frac{7}{8} x$ . We need to divide both sides of the equation by $\frac{1}{}$

Divide both sides of the equation by $\frac{1}{2}$ .
$\frac{\frac{1}{2}(x+9)}{\frac{1}{2}}=\frac{\frac{7}{8} x}{\frac{1}{2}}$

implify the left side of the equation. Dividing by $\frac{1}{2}$ is the same as multiplying by $2$ .
$2 \cdot \frac{1}{2}(x+9) = x+9$

implify the right side of the equation. Dividing by $\frac{1}{2}$ is the same as multiplying by $2$ .
$2 \cdot \frac{7}{8} x = \frac{14}{8} x$

implify the fraction on the right side of the equation.
$\frac{14}{8} x = \frac{7}{4} x$ So, the new equation after dividing both sides by $\frac{1}{2}$ and simplifying the fractions is $x+9 = \frac{7}{4} x$