Question

Solve for x:

a. 9|x/4|-10=8
b. 4+|3x+3|=28
c. 4|x-9|+7=67

Answer 1

a.
`\( x = (32)/(3) \)`

b.
`\( x = (32)/(3) \)`

c.
`\( x = 15 \)`

Step-by-step explanation:

For equation a,
`\(9\left|(x)/(4)\right| - 10 = 8\),` adding 10 to both sides gives
`\(9\left|(x)/(4)\right| = 18\).` Dividing by 9, we have
`\(|x/4| = 2\)` . Solving for
`\(x/4 = 2\)` or
`\(x/4 = -2\)` results in
`\(x = (8)/(1)\)` or
`\(x = -(8)/(1)\),` but only
`\(x = (32)/(3)\)` is valid.

For equation b,
`\(4 + |3x + 3| = 28\),` subtracting 4 yields
`\(|3x + 3| = 24\).` Dividing by 3 gives
`\(|x + 1| = 8\)` . Solving for
`\(x + 1 = 8\)` or
`\(x + 1 = -8\)` gives x = 7 or x = -9, but only x = 4 satisfies the original equation.

Lastly, for equation c,
`\(4|x - 9| + 7 = 67\)`, subtracting 7 gives
`\(4|x - 9| = 60\).`Dividing by 4 results in
`\(|x - 9| = 15\).` Solving for
`\(x - 9 = 15\)` or
`\(x - 9 = -15\)` gives x = 24 or x = -6, but only x = 15 satisfies the original equation. In conclusion, the correct solutions for the given equations are
`\(x = (32)/(3)\)`for a, x = 4 for b, and x = 15 for c.