How do you solve 4x+16=8x-32?

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How do you solve 4x+16=8x-32?

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Answer 1 · 2016-12-30T16:05:12

See explanation below on how to solve this problem:

Explanation:

Step 1) Add the necessary values to each side of the equation to isolate the $x$ $x$ terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

$4 x + 16 - 4 x + 32 = 8 x - 32 - 4 x + 32$ $4x + 16 - color(red)(4x) + color(blue)(32) = 8x - 32 color(red) - color(red)(4x) + color(blue)(32)$

Group and combine like terms on each side of the equation:

$4 x - 4 x + 16 + 32 = 8 x - 4 x - 32 + 32$ $4x - color(red)(4x) + 16 + color(blue)(32) = 8x - color(red)(4x) - 32 color(red) + color(blue)(32)$

$0 + 16 + 32 = 8 x - 4 x - 0$ $0 + 16 + 32 = 8x - 4x - 0$

$48 = 4 x$ $48 = 4x$

Now we can divide each side of the equation by $4$ $color(red)(4)$ to solve for $x$ $x$ while keeping the equation balanced:

$\frac{48}{4} = \frac{4 x}{4}$ $48/color(red)(4) = (4x)/color(red)(4)$

$12 = (color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4))$

$12 = x$

$x = 12$

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How do you solve 4x+16=8x-32?

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