Question

problem 6: here is an equation: \\(\frac{1}{2}(8x - 14) = 3(x - 4)\\)\
what is the solution to this problem?\
\\(\frac{1}{2}(8x - 14) = 3(x - 4)\\)\
\\(4x - 7 = 3x - 12\\)\
\\(4x - 3x = -12 + 7\\)\
\\(x = -5\\)\
solution: \\(x = -5\\)\
problem 7: solve for \\(x\\) in the following equation: \\(8(x - 3) + 7 = -26x\\). show work for full credit.\
solution: \\(x =\\)\
problem 8:\
graph the lines of the equations below, then write the coordinates of their shared solution.\
\\(y = -\frac{2}{3}x + 3\\)\
\\(y = x - 2\\)\
solution coordinates: \\(\underline{(\quad, \quad)}\\)\
\\(x, y\\)

Explanation:

Problem 7

Step1: Expand left-hand side

$8(x-3)+7 = 8x - 24 + 7 = 8x - 17$
Equation becomes: $8x - 17 = -26x$

Step2: Move x terms to left

$8x + 26x = 17$

Step3: Combine like terms

$34x = 17$

Step4: Solve for x

$x = \frac{17}{34} = \frac{1}{2}$

Step1: Set equations equal

$-\frac{2}{3}x + 3 = x - 2$

Step2: Multiply by 3 to eliminate fraction

$-2x + 9 = 3x - 6$

Step3: Move x terms to left, constants right

$-2x - 3x = -6 - 9$

Step4: Combine like terms

$-5x = -15$

Step5: Solve for x

$x = 3$

Step6: Find y with $y=x-2$

$y = 3 - 2 = 1$

Answer:

$x = \frac{1}{2}$

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Problem 8