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Chapter 0: Problem 153

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$5+3(x-4)=8(x-4)=8 x-32$$

Short Answer

Expert verified
The given statement is false, but it becomes true if we rewrite it as \(5 + 3(x - 4) = 3x - 7\) and \(8(x - 4) = 8x - 32\).

Step by step solution

01

Expand the first expression

Expand the first expression as follows: \(5 + 3(x - 4)\) becomes \(5 + 3x - 12\). This simplifies to \(3x - 7\).
02

Expand the second expression

Expand the second expression as follows: \(8(x - 4)\) becomes \(8x - 32\).
03

Compare the expressions

Comparing our results from Step 1 and Step 2, we see that \(3x - 7\) is not equal to \(8x - 32\). So, the equality \(5 + 3(x - 4) = 8(x - 4)\) is false.
04

Re-formulate the statement to make it true

To make the statement true, let's change the statement to read \(5 + 3(x - 4) = 3x - 7\) and \(8(x - 4) = 8x - 32\). Then the statement is true.

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