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UNO [17]
3 years ago
13

Solve for x: 4|2x − 2| 10 = 34. (5 points) x = −4, x = 2 x = 4, x = −4 x = 2, x = −2 x = 4, x = −2

Mathematics
1 answer:
rusak2 [61]3 years ago
7 0
<span>4|2x − 2| + 10 = 34
</span><span>4|2x − 2| + 10 - 10 = 34 - 10
</span><span>4|2x − 2| = 24
</span><span>|2x − 2| = 24/4 = 6
2x - 2 = 6 or 2x - 2 = -6
2x = 6 + 2 or 2x = -6 + 2
2x = 8 or 2x = -4
x = 8/2 or x = -4/2
x = 4 or x = -2

To check for extraneous solutions:
</span>For x = 4: <span>
4|2(4) − 2| + 10 = 34 
4</span><span>|8 − 2| = 34 - 10 = 24
6 = 24/4 = 6       (solution is valid)

</span><span>For x = -2: <span>
4|2(-2) − 2| + 10 = 34 
4</span><span>|-4 − 2| = 34 - 10 = 24
</span></span><span><span><span>|-6| = </span>6 = 24/4 = 6       (solution is valid)  </span>
</span>
Therefore, solutions are x = 4 , x = -2
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