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Determine whether the value ๐‘ฅ=4 makes the following equations true or false.True False ๐‘ฅ+48โˆ’1=06+๐‘ฅ=25โˆ’๐‘ฅ2=โˆ’113(7โˆ’๐‘ฅ)+8=16

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Solution

Sure, let's solve these equations one by one:

  1. ๐‘ฅ+48โˆ’1=0 Substitute ๐‘ฅ=4 into the equation: 4+48-1=0, which simplifies to 51=0. This is false.

  2. 6+๐‘ฅ=2 Substitute ๐‘ฅ=4 into the equation: 6+4=2, which simplifies to 10=2. This is false.

  3. 5โˆ’๐‘ฅ^2=โˆ’11 Substitute ๐‘ฅ=4 into the equation: 5-4^2=-11, which simplifies to 5-16=-11. This simplifies further to -11=-11. This is true.

  4. 3(7โˆ’๐‘ฅ)+8=16 Substitute ๐‘ฅ=4 into the equation: 3(7-4)+8=16, which simplifies to 3*3+8=16. This simplifies further to 9+8=16, and finally to 17=16. This is false.

So, the value ๐‘ฅ=4 makes the third equation true, and the rest false.

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