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QuestionSolve the equation: 4x−168−10=−4\frac{4 x-16}{8}-10=-4.

Studdy Solution

STEP 1

Assumptions1. The problem is a linear equation. . The equation is 4x−168−10=−4\frac{4 x-16}{8}-10=-4.
3. The goal is to solve for xx.

STEP 2

First, we simplify the fraction in the equation.4x−168\frac{4 x-16}{8}

STEP 3

We can simplify this fraction by dividing both the numerator and the denominator by.
x−168=(x−)8\frac{ x-16}{8} = \frac{(x-)}{8}

STEP 4

Further simplifying the fraction, we get4(x−4)8=12(x−4)\frac{4(x-4)}{8} = \frac{1}{2}(x-4)

STEP 5

Now, we substitute this simplified fraction back into the original equation.
12(x−4)−10=−4\frac{1}{2}(x-4)-10=-4

STEP 6

Next, we can distribute the 12\frac{1}{2} in the equation.
12x−2−10=−4\frac{1}{2}x -2 -10 = -4

STEP 7

We simplify the equation by combining like terms.
12x−12=−4\frac{1}{2}x -12 = -4

STEP 8

Next, we add12 to both sides of the equation to isolate the term with xx.
12x=−4+12\frac{1}{2}x = -4 +12

STEP 9

olving the right side of the equation, we get2x=8\frac{}{2}x =8

STEP 10

Finally, we multiply both sides of the equation by2 to solve for xx.
x=8×2x =8 \times2

STEP 11

olving the right side of the equation, we getx=16x =16So, the solution to the equation is x=16x =16.

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