Math

QuestionSolve for xx in the equation x2+x7=9\frac{x}{2}+\frac{x}{7}=9.

Studdy Solution

STEP 1

Assumptions1. The equation is x+x7=9\frac{x}{}+\frac{x}{7}=9 . We are solving for x

STEP 2

The first step to solve this equation is to get rid of the fractions. We can do this by finding a common denominator for2 and7, which is14.
Multiply each term by14 to eliminate the fractions.
14x2+14x7=14914 \cdot \frac{x}{2} +14 \cdot \frac{x}{7} =14 \cdot9

STEP 3

implify each term.
7x+2x=1267x +2x =126

STEP 4

Combine like terms on the left side of the equation.
9x=1269x =126

STEP 5

Now, to solve for x, divide both sides of the equation by9.
x=1269x = \frac{126}{9}

STEP 6

Calculate the value of x.
x=1269=14x = \frac{126}{9} =14The solution to the equation x2+x=9\frac{x}{2}+\frac{x}{}=9 is x=14x =14.

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