QuestionSolve the equation: $\frac{2}{7}(5 x+4)=\frac{1}{2}(3 x-10)+4$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $\frac{}{7}(5 x+4)=\frac{1}{}(3 x-10)+4$ . We are solving for the variable $x$
3. The equation is linear, meaning there is only one solution for $x$

STEP 2

First, we need to distribute the fractions on both sides of the equation.
$\frac{2}{7}(5 x+4)=\frac{1}{2}( x-10)+4$

STEP 3

istribute the $\frac{2}{7}$ on the left side of the equation.
$\frac{2}{7} \cdot5x + \frac{2}{7} \cdot = \frac{1}{2}(3 x-10)+$

STEP 4

implify the left side of the equation.
$\frac{10}{7}x + \frac{8}{7} = \frac{1}{2}(3 x-10)+4$

STEP 5

istribute the $\frac{1}{2}$ on the right side of the equation.
$\frac{10}{7}x + \frac{8}{7} = \frac{1}{2} \cdot3x - \frac{1}{2} \cdot10 +4$

STEP 6

implify the right side of the equation.
$\frac{10}{}x + \frac{8}{} = \frac{3}{2}x -5 +4$

STEP 7

implify the right side of the equation further.
$\frac{10}{7}x + \frac{}{7} = \frac{3}{2}x -1$

STEP 8

To solve for $x$ , we need to isolate $x$ on one side of the equation. Let's start by subtracting $\frac{3}{2}x$ from both sides of the equation.
$\frac{10}{7}x - \frac{3}{2}x + \frac{8}{7} = -1$

STEP 9

To subtract fractions, we need to have a common denominator. The least common denominator of7 and2 is14. So, let's convert the fractions to have the denominator14.
$\frac{20}{14}x - \frac{21}{14}x + \frac{8}{7} = -$

STEP 10

Now, subtract the fractions on the left side of the equation.
$-\frac{}{14}x + \frac{8}{7} = -$

STEP 11

Next, subtract $\frac{8}{7}$ from both sides of the equation to isolate $x$ .
$-\frac{}{14}x = - - \frac{8}{7}$

STEP 12

implify the right side of the equation.
$-\frac{}{14}x = -\frac{15}{7}$

STEP 13

To solve for $x$ , divide both sides of the equation by $-\frac{}{}$ .
$x = -\frac{15}{7} / -\frac{}{}$

STEP 14

implify the right side of the equation.
$x = \frac{}{7} \cdot \frac{14}{}$

STEP 15

Calculate the value of $x$ .
$x = \frac{15 \cdot14}{7} =30$ So, the solution to the equation is $x =30$ .

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