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QuestionSolve the equation: 27(5x+4)=12(3x−26)+12\frac{2}{7}(5 x+4)=\frac{1}{2}(3 x-26)+12. What is xx? A. x=□x=\square B. All real numbers. C. No solution.

Studdy Solution

STEP 1

Assumptions1. The equation is 7(5x+4)=1(3x−26)+12\frac{}{7}(5 x+4)=\frac{1}{}(3 x-26)+12 . We are solving for xx
3. All operations are performed according to the order of operations (PEMDAS/BODMAS)

STEP 2

First, we need to distribute the fractions on both sides of the equation.27(5x+4)=10x7+87\frac{2}{7}(5 x+4) = \frac{10x}{7} + \frac{8}{7}12(x−26)=x2−13\frac{1}{2}( x-26) = \frac{x}{2} -13

STEP 3

Now, replace the original equation with the distributed terms.
10x7+87=3x2−13+12\frac{10x}{7} + \frac{8}{7} = \frac{3x}{2} -13 +12

STEP 4

implify the right side of the equation.
10x7+87=3x2−1\frac{10x}{7} + \frac{8}{7} = \frac{3x}{2} -1

STEP 5

To make the equation easier to solve, we can multiply every term by14 to get rid of the fractions.
14⋅10x7+14⋅87=14⋅3x2−14⋅114 \cdot \frac{10x}{7} +14 \cdot \frac{8}{7} =14 \cdot \frac{3x}{2} -14 \cdot1

STEP 6

implify the equation.
20x+16=21x−1420x +16 =21x -14

STEP 7

Now, we can start to isolate xx. First, subtract 20x20x from both sides of the equation.
16=x−1416 = x -14

STEP 8

Finally, add 1414 to both sides of the equation to solve for xx.
x=16+14x =16 +14

STEP 9

Calculate the value of xx.
x=30x =30So, the correct choice is A. x=30x=30.

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